Algebraic terms. Applied Mathematics

Alekseenko Marta, Soskov Dmitry

Etymological dictionary of mathematical terms.

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Studying any subject is more interesting when you understand the meaning of the terms. At the same time, paying attention to the semantic meaning and origin of a particular word, the memorization process becomes almost invisible and the further correct use of this word does not cause difficulties.

Many mathematical terms already “contain a definition” in their name, i.e. carry an understandable semantic load (words that are original). Such as: “triangle”, “segment”. But what about words that are borrowed from another language and sound completely incomprehensible? “Abscissa”, “ordinate”, “applicate” - for an ignorant person these words mean nothing. And if you understand the etymology of these words, then everything becomes clear.

Unfortunately, there is practically no interpretation of the terms in mathematics textbooks. And etymological dictionaries do not always contain an interpretation of a particular word. Specialized dictionaries are not always available. Using Internet resources is also not always convenient - it takes too much time and may contain unreliable or incomplete information. Therefore, the idea arose to create a small dictionary that would include mathematical terms often used in mathematics lessons.

Creating such a dictionary is, first of all, collecting and analyzing information. Various dictionaries, textbooks, as well as information posted on Internet pages were studied. When using Internet resources you often encounter different interpretations the same word. This is explained by the fact that the same term is borrowed from different languages ​​- hence the different translations. And if you “dig” deeper and come to the original meaning of a given word (this is, as a rule, Latin or more ancient Greek), then the true meaning of the word becomes clear. Also, Internet resources do not always have a link to the etymological dictionary from which the interpretation is taken. In this case, the search continued.

To determine which words should be included in the dictionary, it was necessary to remember the terms already studied, and also turn to high school textbooks to find out which terms were yet to be familiarized with.

The etymology of many terms is familiar to us from mathematics lessons. Some words that are already familiar and understandable sometimes surprised us with their translation. For example, the word “cone” is Greek. the word konos - “pin”, “cone”, “top of a helmet” or “cube” - Greek. the word kubos means “dice”. The word “numbering” has never raised questions at all, but it turns out that it comes from the Latin word numero - “I count.” Thus, by collecting and analyzing information, we learned a lot of new and interesting things.

After a sufficient number of words were collected to create a dictionary, the question arose: what should this dictionary look like? In electronic format – not always accessible and convenient to use. In the form of printed sheets inserted into a folder, it doesn’t look much like a dictionary. And we decided to create a real dictionary - in the form of a book. But designing it in book form is not yet a real dictionary. We studied in more detail how dictionaries are compiled, including etymological ones. We found out that it is necessary to indicate the decoding of the available abbreviations, the sources where the information was taken from, and also compose explanatory note. Some dictionaries contain the Latin and Greek alphabets, we also decided to include them in the dictionary. While collecting information, we discovered a table of the origin of mathematical terms and their creators - it also ended up in the dictionary.

Thus, the result of our work was the “Etymological Dictionary of Mathematical Terms,” consisting of borrowed words, which will help both students and teachers.

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ETYMOLOGICAL DICTIONARY

MATHEMATICAL TERMS

Math project

"Etymological Dictionary of Mathematical Terms"

Project Manager:

Ivanova A.I. – teacher of mathematics and computer science

Project participants:

Students of grade 8B

Alekseenko Marta

Soskov Dmitry

Shmatchenko Victoria

The project was defended

Within the framework of a scientific and practical conference

based on State Educational Institution Secondary School No. 436

Sources:

1. Etymological dictionary of the Russian language for schoolchildren, Ekaterinburg: U-Factoria; Vladimir: VKT, 2008, comp. M.E.Ruth

2. Brief dictionary foreign terms in mathematics

Book for students

E. Polovinkina S. Shakirova

3. Algebra and beginnings of analysis, textbook for grades 10-11 of high school, A.N. Kolmogorov et al.

4. Internet resources:

1. http://ru.wiktionary.org/w/index.php

2. http://www.phro.ru

. http://dic.academic.ru/dic.nsf/bse/154726/Etymology

7. http://maxfas.ru

Greek letters	Their name		Letters	Their name
Αα	alpha
Ββ	beta			bae
Γγ	gamma			tse
Δδ	delta			de
Εε	epsilon			e, e
Ζζ	zeta			ef
Ηη	this			uh, same
Θθ	theta			ha, ash
Ιι	iota
Κκ	kappa			Yot, zhi
Λλ	lambda			ka
Μμ	mu			ale
Νν	nude			Em
Ξξ	xi			en
Οο	omicron
Ππ	pi			pe
Ρρ	ro			ku
Σσ	sigma			er
Ττ	tau			es
Υυ	upsilon			te
Φφ	fi
Χχ	hee			ve
Ψψ	psi			double-ve
Ωω	omega			X
				igrek, upsilon
				zeta, zeta

Explanatory note.

Studying any subject is more interesting when you understand the meaning of the terms. At the same time, paying attention to the semantic meaning and origin of a particular word, the memorization process becomes almost invisible and the further correct use of this word does not cause difficulties.

Many mathematical terms already “contain a definition” in their name, i.e. carry an understandable semantic load (words that are original). Such as “triangle”, “segment”. What about borrowed words? “Abscissa”, “ordinate”, “applicate” - for an ignorant person these words mean nothing. And if you understand the etymology of these words, then everything becomes clear!

This dictionary contains terms that are quite often found in mathematics lessons (and not only). The words found in the dictionary are only borrowed. Their interpretation will help you understand such a difficult subject as mathematics.

The first column indicates the word, the language from which the word was borrowed, the scientist who first used the term, and the year it appeared. The second column contains the translation and interpretation of the term. The dictionary is also equipped with a table of the origin of various mathematical symbols and Greek and Latin alphabets.

Abscissa French via Lat.	Abscissa - “segment”, “cut off”
Axiom ancient Greek	axioma - “dignity”, “respect”, “authority”. Originally the term had the meaning of “self-evident truth.”
Algebra Arab. Muhammed ben Musa al-Khwarizmi, 11th century	“ aljabr ” meant the operation of transferring the subtracted from one part to another and its literal meaning is “replenishment”.
Algorithm lat.	algorizmus, algorithmus - in honor of the Uzbek scientist Al-Khorezmi, who in the 9th century first formulated the rules for performing arithmetic operations using the decimal number system
Analysis Greek	aualusiz - “decision”, “resolution”.
Amplitude lat.	amplitude - “magnitude, significance”, from amplus “vast, wide; big".
applicata lat.	applicata - “attached” This means that the third coordinate of the point is applied to the first two (abscissa and ordinate)

List of abbreviations

English - English

Arab. – Arabic

Greek

– Greek

other - ancient

Italian

– Italian

lat.

– Latin Greek	German - German fr - french Apothem apothema,
apo – “from”, “from” theme – “attached”, “delivered”.	Literal meaning of the word: to put off Argument“sign”, “argument”
Arithmetic Greek	ariumoz - "number". The word entered the Russian language in the 16th century.
arcsine lat. XVIII century	arcsinus arcus "arc" sinus "bend". Arcsine x – an angle or arc whose sine is equal to X .
Asymptote Greek	asymptotes a – negation sumtwtoz – “coinciding”, “merging” The literal meaning of the word is “non-matching”.

	Square root of –1	L. Euler	1777
x,y,z	Unknown quantities	R.Descartes	1637
	Vector	O. Cauchy	1853
	Equality	R.Record	1557
	More less	T. Garriott	1631
	Comparability	K.Gauss	1801
	Parallelism	W.Outred	1677
	Perpendicularity	P. Erigon	1634
Arabic numerals	Math. signs	Indian mathematicians	5th century
	Module	K. Weierstrass
Roman numerals	Math. signs	Russian mathematicians	5th century BC
≤ ≥	Non-strict inequalities	P. Bouguer	1734
	Square brackets	R.Bombelli	1550
	Round brackets	N. Tartaglia	1556
	Braces	F. Viet	1593

arcsin, arctg	Arcsine, arctangent	J. Lagrange	1772
dx, ddx,..d 2 x	Differential	G. Leibniz	1675
∫ydx	Integral	G. Leibniz	1675
	Derivative	G. Leibniz	1675
	Definition integral	J. Fourier	1819-1822
	Sum	L. Euler	1755
	Factorial	H. Crump	1803
	Limit	W.Hamilton	1853
Lim, lim n=∞ n→∞	Limit	Many mathematicians	Early 20th century
f(x)	Function	I. Bernoulli, L. Euler	1718, 1734
	Infinity	J. Wallis	1655
	Ratio of circumference to diameter	W. Jones, L. Euler	1706, 1736

Gymnasium Greek through Lat.	Greek γυμνασιον from lat. gymnasium - a place for physical exercise. Meaning " educational institution" arose much later, when mental development began to be given more importance.
Hyperbola Lat. via Greek. Apollonius of Perga	lat. hyperbola, Greek ύπερβολη ύπερ - “through, over” βολλω - “throw”
Hypotenuse Greek	upoteiuw - "pull on"; literal meaning of the word upoteiuosa - “tight”, comes from the method of constructing a right-angled Egyptian triangle by pulling a rope. The ancient Greek scientist Euclid (3rd century BC) wrote instead of this term, “the side that subtends a right angle.”
bar chart ancient Greek	ἱστός - “mast; fabric” (from chap.ἵστημι "to put") γραμμή - “dash, line” (fromγράφω “I write, I draw, I describe”).
Homothety Greek	omos - “equal”, “identical” and oetoz - “installed”, “located” The literal meaning of the word is “equally located.”
Degree lat.	degree - “step”, “step”.
Schedule Greek	graphikos - “inscribed.”

Decimeter fr. via lat. end of the 18th century	decimus - tenth meter - meter Literal meaning of the word: “tenth of a meter”
Diagonal Greek beginning of the 18th century	diagonios dia – “through” gonium – “angle”. The literal meaning of the word is “passing through the corner.”
Diameter Greek	diametroz - “diameter”.
Discriminant lat. Sylvester.	discriminare - “disassemble”, “distinguish”. Literal meaning of the word: “discriminator”
Fraction Leonardo of Pisa (1202)	In all languages, a fraction is called a “broken” number. Latin word fractura - derived from frango - “break”, “break”. The names numerator and denominator are given by Maxilus Plakudus (13th century).

Table of the origin of basic mathematical symbols.

Sign	Its meaning	Who entered	When a character is entered
	addition	J. Widman	Late 15th century
	subtraction	J. Widman	Late 15th century
	multiplication	W.Outred	1631
	multiplication	G. Leibniz	1698
	division	G. Leibniz	1684
a 2 , a 3 ,.. a n	degrees	R.Descartes	1637
	root	H. Rudolf, A. Giror	1525, 1629.
Log, log	logarithm	I. Kepler	1624
	sinus	B. Cavalieri	1632
	cosine	A. Euler	1748
	tangent	A. Euler	1753

Equivalence lat. Dubois Raymond 1870	aequs - “equal” valens - “having strength”, “strong”. The literal meaning of the term “equivalent”.
Exhibitor lat. Stiefel 1553	exponentis - “showing”.
Extremum lat. Dubois Raymond 1879	extremum - “extreme”, “last”.
Ellipse Greek Apollonius of Perga 3rd century BC	elleiyiz - disadvantage.

Dozen fr.

douzaine from douze - “twelve”

Igrek fr.	i Greek - “and Greek”
Icosahedron Greek It is believed that the name was given by Tiet, who discovered it. Euclid and Heron have the term.	eixosi - “twenty” edra - “base”. The literal meaning is “twenty-sided”.
Index lat. beginning of the 18th century	Index – “pointer”.
Integral fr. via lat. Bernoulli first used it in 1690.	integro – “restore” or integer – “whole”.
Interval lat. The modern designation first appeared in 1909 by the German scientist Kovalevsky.	intervallum - “interval”, “distance”

Calculator German via lat.	German kalkulator lat.
calculator – “to count”. Greek	Leg kauetoz
- “dropped perpendicular”, “plumb line”. Greek	Square quadratus
- “quadrangular”. lat. Collinearity Hamilton, Gibbs	(circa 1843) co - “with”, “together”, lianeris - “linear”
the literal translation is “solinear”. lat. Coplanarity	W. Hamilton 1843 con, com – “together” planum
- “plane”. German via lat.	Abstract conspectus

- “review, review, view” lat.	Constant constants
- “constant”, “unchangeable”. Greek Cone	The term received its modern meaning from Euclid, Aristarchus, Archimedes kwnoz - “pin”, “ Pine cone
”, “helmet tip”, “pointed object Coordinate late lat.	Leibniz, 1692. Coordinātiō co- (cum-) “with, together” ordinātiō
- “distribution, location, definition (of place).” lat. Root	John of Seville (1140), Robert of Chester (1145) and Gerard of Cremona (1150) IN Latin“side”, “side”, “root” are expressed by the same word radix“side”, “side”, “root” are expressed by the same word The terms “radical” and “root” arose, which entered mathematics thanks to the translation of Euclid’s “beginnings” from Arabic into Latin.

Cosine lat. Genter 1620	comlemendi sinus - “additional sine”.
Cotangent lat. Abu-l-Wafa, 10th century	complementi tangens – additional tangent, or from lat. words cotangere – “to touch” (tangent – ​​to touch).
Coefficient lat. Viet 1591	co (con, cum)- “with”, “together” and effeciens - “producing”, “constituting the cause of something” The literal meaning is “helper.”
Cube Greek introduced by the Pythagoreans	kuboz - “dice”, since it had the shape of a cube, the name was transferred to any body of the same shape.

Lecture German via lat.	German lecture - “lesson” lat. lectio (leger) - “reading (to read)”
Lemma Greek	lemma - “assumption”, “previous position”. In Archimedes and Proclus, the term already has the meaning of “auxiliary theorem”.
Line Lat.	linea - “flax”, “thread”, “cord”, “rope”.
Protractor lat.	transortare – “transfer”, “shift”.
Trapezoid Greek Posidonius	trapezwu - “table”.
Trigonometry Greek Pitiscus1595	trifwuou - “triangle” metrew - “measuring.” Literally meaning “the science of measuring triangles.”

Table lat.	tabula - “board”, “table for writing”, “table”.
Tangent lat. Thomas Finke 16th century	Tangents - “tangential” Tangent as the shadow of a vertical pole was introduced by the Arab mathematician Abu-l-Wafa in the 10th century.
Theorem Fr. through other Greek Archimedes	fr. theorema from Greek. qewrhma the word means “spectacle”, “performance”. In Greek mathematics, this word began to be used in the sense of “truth accessible to contemplation.”
Theory Greek	qewria – “research”, “scientific knowledge”.
Notebook Greek	τετραζ - “four”, a sheet of paper folded in four and cut to form a book.
Tetrahedron Greek Euclid	tettrrea – “four” edra – “base”. Literally meaning “tetrahedron”.
Dot	The word comes from the verb “ poke ” and means the result of an instant touch, injection.

German via fr.

German marschroute

fr. marsche - “movement, procession”

fr. routе - “road, path”

The literal meaning of the word is “path to follow”

Scale

German

maßstab

mas – “measure”

stab - stick."

Mathematics

Greek

matematike

matema, mauhma - “science”, “teaching”, in turn, comes from the verb mauanw - the original meaning is “learn through reflection.”

Median

lat.

medius - “average”.

Million	The word was first introduced in Italy in the 14th century to denote a large thousand i.e. 1000². Latin mille - “thousand”.
Minimum lat.	minimum - " least ".
Minus lat. Italian mathematics of the 14th century	minus - “less”.
Minute, second, third lat.	minuta prima - “first beat”, minuta secunda - “second share”, minuta tertia- "third beat" For shortening, the first beat began to be called “minute” (beat), the second – “second”, the third – “third”.
Module lat. R. Cots,	modulus - “measure”, “magnitude”.
Monotone lat. Neumann 1881	monozutonoz - “tension”, “current”. Literal meaning: monotony.

Sinus Lat. through ind. Aryabhata 499 The modern designation sin was introduced by the Russian scientist Euler in 1748.	sinus – “bend”, “curvature”, “sinus”. In the IV-V centuries. called " ardhajiva" (ardha – “half”,jiva- “bow string”). Arab mathematicians in the 9th century. word "jibe" - "convexity". When translating Arabic mathematical texts in the 12th century.
System Greek	susthma-“made up of parts.”
Scalar lat.	scalaris- stepped (scale)
Stereometry Greek Aristotle.	stereoz-“volumetric” Andmetrew- “I measure”, the literal meaning is “measurement of volumes”.
Sum lat. 15th century	summa- “main point”, “essence”, “total”, “sum”, “highest, total number” fromsummus"higher". The literal meaning of the word is “total quantity”
Sphere Greek Plato, Aristotle.	sfaira- “ball”, “ball”.

ABOUT

P

Parabola GreekApollonius of Perga	parabola- "application "
Parallelism Greek school of Pythagoras 2500 years ago	parallhloz- “walking next to each other”, “carried next to each other”.
Parallelogram Greek Euclid	parallelos– “parallel” andgramma- “line”, “dash”.
Parallelepiped Greek Archimedes and Heron.	parallelos- “parallel” andepipedos- “surface”.
Parameter ancient Greek	parameters- “measuring”.
Perimeter Greek Archimedes	perimetroe peri- "near" metreiu- "to measure".
Period. ancient Greek	peri -“about”, “around” odoz- "way". Means “way around”, “detour”.
Perpendicular lat.	perpendiculum- “plumb line”, which in turn is produced fromperpendre- “to weigh.”
Pyramid Greek Euclid	per me ous- “side edge of the structure.”
Poster German via French	Germanposterfrom fr.placard– “poster”, from Old Frenchplaquier- “stick”
Planimetry Greek lat.	Latincon, com – “together”- “flatness” Greekmetrew- "to measure "
Plus 14th century Italian algebra	plus- "more ".
Prism Greek Archimedes, Euclid	prisma– “sawed off piece”, “sawed off part” (priv - “saw”).
Example Greek Greek mathematicians	primus- "first ".
Progression lat.	progredior- “I’m moving forward”;progressio -“moving forward”, “success”, “gradual strengthening”.
Projection lat.	projectio-“throwing forward”, which in turn is formed from the verbprojiciere- “throw away”, “throw away”.
Derivative fr. Lagrange 1797	The word ableiten, derivafe was first used in the correspondence of Newton and Leibniz (1675-1677).
Proportion lat.	pro“from”, “with” portio- "size " The literal translation is “correlation, proportionality”.
Percent lat.	pro“with”, “from” centum"one hundred" The literal meaning of the word is “from a hundred”

abscissa- segment) of point A is the coordinate of this point on the OX axis in a rectangular coordinate system

Axiom

(ancient Greek ἀξίωμα - statement, position) - a statement accepted as true without evidence, and which subsequently serves as a “foundation” for building evidence within the framework of a theory, discipline, etc. .

applicata

coordinate of a point on the OZ axis in a rectangular three-dimensional coordinate system.

Asymptote

(from Greek ασϋμπτωτος - non-coinciding, not touching) a curve with an infinite branch - a straight line with the property that the distance from a point on the curve to this straight line tends to zero as the point moves away along the branch to infinity. The term first appeared in Apollonius of Perga, although the asymptotes of a hyperbola were studied by Archimedes

For a hyperbola, the asymptotes are the abscissa and ordinate axes. A curve can approach its asymptote while remaining on one side of it

Vector

directed segment - ordered pair of points

Hyperbola

(ancient Greek ὑπερβολή , from ancient Greek. βαλειν - "throw", ὑπερ - “over”) - geometric locus of points M Euclidean plane, for which the absolute value of the difference in distances from M up to two selected points F 1 and F 2 (called foci) constantly.

Discriminant

quadratic equation ax2 + bx + c = 0 expression b2 4ac = D by the sign of which one judges whether this equation has real roots (D ? 0)

Integral

a natural analogue of the sum of a sequence. Informally speaking, the (definite) integral is the area of ​​the subgraph of a function, that is, the area of ​​a curved trapezoid.
The process of finding the integral is called integration. According to the main theorem of analysis, integration is the inverse operation of differentiation

Irrational numbers

is a real number that is not rational, that is, which cannot be represented as a fraction, Where m- integer, n - natural number

Constant

a quantity whose value does not change; in this it is the opposite of a variable.

Coordinate

A set of numbers that determine the position of a specific point

Coefficient

a numerical factor for a literal expression, a known factor for one degree or another of an unknown, or a constant factor for a variable value.

Lemma

a proven statement that is useful not in itself, but for proving other statements

Module (absolute value)

continuous piecewise linear function defined as follows:

Vector module

length of the corresponding directed segment

Ordinate

(from lat. ordinatus- located in order) of point A is the coordinate of this point on the OY axis in a rectangular coordinate system

Parabola

second order curvegraph of equation (quadratic function)y = ax 2 + bx + c

Proportion

(lat. proportionio- proportionality, alignment of parts), equality of two relations, i.e., equality of the form a : b = c : d , or, in other notations, equality(often read as: "a refers to b as well as c refers to d"). If a : b = c : d, That a And d called extreme, A b And c - averagemembers of the proportion.

n - natural number.

Theorem

(Greek theorema, from theoreo - I consider), in mathematics - a proposition (statement) established by means of proof (as opposed to an axiom). A theorem usually consists of a condition and a conclusion

Factorial

denoted by n!, pronounced en factorial) - the product of all natural numbers up ton inclusive:

Function

"law" according to which each element of one set (called domain of definition) is put into correspondence with some element of another set (called range of values).

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This article contains a glossary of mathematical terms and definitions to simplify your search for a specific formula among many arithmetic lexicon. In the ocean of mathematics, there are countless drops of different terms, words, definitions and glossary. When you start searching for a specific topic and its meaning, you seem to get lost in the wonderful world of numbers. Mathematics is the queen of all sciences and this is reflected in the use of numbers in our daily lives. There is hardly any field, be it biology, physics, chemistry, astronomy, or economics, where numbers do not come into play. Our life was almost at a standstill without this theme. To help you look up the expressions you need, this article is a glossary of mathematical terms and definitions, which are presented in alphabetical order below.

Mathematical definitions are derived from extensive research and theory. If the explanation is not proven to be the correct expression, it is always an area of ​​investigation and debate. The terminology recorded here has been collected from many different branches such as Algebra, Trigonometry, Measurement, Geometry, Calculus, etc.

Branches

This field has applications in almost every aspect of life and work. The operations of addition, subtraction, multiplication, and division form the platform for higher order. Kinematics, Dynamics, linear algebra, ring theory, calculus and integration of the most popular scientific fields. The magical world of permutations and combinations, not to mention probability, has its own wonderful applications in the real world. Read the articles below to enter this wonderful world.

A | B | C | D | E | F | G | H | And | JJ | K | L | M | N | About | P | M | R | C | T | U | X | Ш | X | G | Z |
A

Similarities of AA

According to AA similarity data, if two angles of a triangle are equal to two angles of another triangle, then the triangles are similar to each other.

AAS Congruence

AAC congruence is called angle-angle-side congruence. If there are two pairs of corresponding angles and a pair of corresponding opposite sides that are equal in measure, then the triangle is called congruent.

Abscissas

The X-coordinate of a point in a coordinate system is called the abscissa. For example, in an ordered pair n(2, 3, 5), 2 we will call the abscissa of the point p. In mathematical language this will be called the length of the point (p) relative to the x-axis.

Absolute Convergence

A series that converges when all its expressions are replaced by their absolute values. To check if a series is absolutely convergent, then it is only required to replace any subtraction in the series with an addition. In the series N=1Σн=∞is absolutely convergent if the series n=1Σн= ∞ |аn| converges.

Absolute Maximum

The highest point of a function or relationship in an entire domain is called the absolute maximum. First and second derivative tests are commonly used to find the absolute maximum of a function.

Absolute Minimum

The lowest point of a function or connection in an entire domain is called the absolute minimum. First and second derivatives are the most commonly used methods for finding the absolute minimum. The global minimum is also called the absolute minimum.

Absolute Value

The general concept of absolute value is that it makes a negative number positive. The absolute value is called the mod value. The absolute value of a number (say x) is denoted by |x|. Remember, absolute value uses bars, so don't use parentheses or any other symbol, otherwise the meaning will change. Simply put, |-7| = 7 and |7| = 7. Positive numbers and zero remain unchanged in absolute value. A better and more accurate way to understand it is that the absolute value of a number denotes the distance between the number and the origin. Thus, |x-a| = b, where b>0, says that the quantity x-a-z units from 0, x-a-b units to the right of 0(origin) cotton units to the left of 0 (start).

Absolute value of a complex number

The absolute value of the complex number |a + b| = √A2 + B2. The absolute value of a complex number is the distance between the initial and complex planes. For a complex number in the form p(arccosineθ + sinθ), modulus p, i. e. circle radius value cut out trigonometric equation.

Acceleration

The rate at which speed changes over time is called acceleration. Mathematically, the second derivative of an object's distance is called acceleration.

Accuracy

The measure of tightness of the value of the actual value of the result is called precision.

Sharp corner

An angle whose measure is less than 900 is called an acute angle.

Acute Triangle

A triangle in which all interior angles are acute is known as an acute isosceles triangle.

Rule of Addition of Probabilities

The addition rule is designed to find out the probability of one or both events occurring.

If p(a) AND P(B) are mutually exclusive events, then the probability P(A or B) = P(A) + P(B), then P(A or B) = P(A) + P( B) - P(A AND B).

Additive Matrix Inversion

If the sign of each element of the matrix changes, then the matrix is ​​called the inverse of the original matrix. If there is a matrix, then it will be an inverse matrix. If you add a matrix and its inverse, the sum will be zero, since each element in the original matrix is ​​the negative of the others.

Property addition equality

Simply put, the States are additive assets that can be added to both sides of the equation. For example, x - 3 = 5 - The same as x - 3 + 3 = 5 + 3.

Adjacent Angles

If two angles share a common vertex and a common plane and even on the same side, and if they do not intersect, or one of the angles is not contained in the other, then the angles are called adjacent angles.

Adjoint Matrix

When we transpose the co-coefficient of the original matrix, it is called an adjoint matrix.

Affine Transformations

Affine transformation refers to a combination process that can be performed on any coordinate system, such as translation, rotation, horizontal and vertical stretching and shrinking. It should be borne in mind that parallelism and colinearity are invariant under any type of transformation.

Aleph Null

The first letter of the Hebrew alphabet, Aleph (א), denotes the cardinal number of an infinite countable set. In principle, the subscript א0 is typically used to denote the elements of an infinitely countable set.

Algebra

This is a branch of pure mathematics that uses alphabets and letters as variables. Variables are unknown quantities whose values ​​can be determined using other equations. For example, 3x - 7 = 78, is an algebraic equation with one unknown variable (here x). Now, using algebra methods we can solve the equation. Read more about algebra tips.

Algebraic Numbers

All rational numbers are algebraic numbers. Numbers that are roots of polynomials with integer coefficients and under surd are also included as algebraic numbers. Any number that is not the root of a polynomial with integer coefficients is not an algebraic number. These numbers are called transcendental numbers. e and Π are called transcendental numbers.

Algorithm

The algorithm is simple, step by step, to arrive at a solution to any problem.

Alpha is the 1st letter of the Greek alphabet. It is denoted (in upper case) and α (in lower case). It is often used in science as a variable to represent angles, etc.

Alternating Angles

When two or more parallel lines are cut transversely, the angles formed in alternative directions to each other are called alternative angles.

Alternative External Corners

When two or more parallel lines are cut at transverse, alternative angles, outside one another is called an alternative exterior angle.

Alternative Internal Angles

When two or more rows are cut transversely then alternating angles that lie interior to each other are called alternate interior angles.

Alternative Series

A variable series is a series that consists of alternating positive and negative sides.
The alternating sequence has the form:
1 - ½ + 1/3 - ¼ + 1/5. to infinity.

Alternation Other Series

The alternating sequence looks like this:
n = 1 ∑н = ∞ = (-1)п+1ан = А1 - А2 + А3 + .

If the series converges to s, using alternating series of trials, then the rest,
РН = з - к=1∑н(-1)к+1ak, for all N ≥ Н, is called the rest series variable.

In addition, |pH| ≤ in + 1.

Height is the shortest distance from the base to the top of shapes such as cones, triangles, etc.

Cone height

The distance between the top of a cone and its base is called the height and altitude of the cone.

Cylinder height

The distance between the circular bases of a cylinder or the length of a linear segment between two of its bases is called the height of the cylinder.

Parallelogram height

The distance between opposite sides of a parallelogram is called the height of the parallelogram.

Prism height

The distance between the bases of the prism is called the height of the prism.

Pyramid height

The distance from the top of the pyramid to the base is called the height of the pyramid.

Trapezoid height

The distance between the bases of a trapezoid is called the height of the trapezoid.

Triangle height

The shortest distance between the vertex of a triangle and the opposite side is called the height of the triangle.

Amplitude

It measures half the distance between maximum and minimum range. For example, if we consider a sine wave, then ½ the distance between the positive and negative curves is called the amplitude. It should be remembered that only periodic functions with a limited spectrum have amplitudes.

Analytic geometry

Analytical geometry is a branch that deals with the study of geometric shapes using coordinate axes. Points are plotted and with the help of glasses you can easily find the necessary information.

Analytical Methods

If you are asked to solve a problem analytically, this means that you should not use a calculator. Analytical methods are used to solve problems using algebraic and numerical methods.

An angle is defined as the figure formed by touching the ends of two rays. In other words, it means the separation of two rays emanating from a common point.

Bisector

The line that divides an angle into two equal parts is called the angle bisector.

Depression angle

The angle below the horizontal line that an observer must see in order to site an object is called the angle of depression. To better understand this, consider an observer at the top of a rock, when he has in mind an object at some distance from the base of the rock, the angle subtended by him will have to accompany the construction object is called the angle of depression.

Elevation angle

The angle of elevation geometrically coincides with the angle of depression. If a person observes an object at some height, then he must raise its line of sight above the horizontal level, this is called the elevation angle.

Line angle

The angle subtended by the line with the x-axis is called the angle of inclination of the line. The tilt angle is always measured in the counterclockwise direction, which means the x-axis is positive. The tilt angle is always between 00 and 1800.

The area between the two concentric circles of the ring (say) is called the annulus fibrosus.

Counterclock-wise

Look in the opposite direction to the movement. In this case, it is the assumption that counterclockwise always measures positive.

Antiderivative of function

If F(x) = 2x2 + 3, then its derivative F"(x) = 4x. Here 4x is called the antiderivative of the function f(x).

Antipodean Points

In three dimensions, points that are diametrically opposite on a sphere are called antipodal points.

Apothem is the same as inscribed in an inscribed circle in a regular polygon. In other words, this would mean the distance from any of the midpoints of the sides of the polygon to the center of the polygon.

Approximation of differentials

According to the rule of approximation of differentials, the value of the function is approximated and the principles of derivation are used in this method. The formula used in the approximation of differentials is Ф(Х + ∆Х) = Ф(х) + ∆у = F(Х) + Ф"(х)∆х, where f"(x) is a differential function.

Curve Arc Length

The length of the Curve line is called the arc length. There are three formulas for determining the arc length of a Curve. There are rectangular shape, polar shape and parametric shape that can be used.
Rectangular shape - DS = 1/2
Parametric form - DS = (DH/DT)2 + (DU/DT)2dt]1/2
In polar form - DS = [P2 + (d/dƟ)2]1/2
Area of ​​a circle
The area of ​​a circle is determined by the formula ΠР2.

The inverse cosine function is called the arccos function. For example, cos-1(1/2) (read as cos is the inverse half) or "into the corner, the cosine of which is equal to ½. As we all know, that is nothing but 600.

The inverse of cosec is called arccosec. For example, cosec-1(2) means that the angle whose cosecant is equal to 2. The answer is 300. It should be noted that there can be many more angles with a cosecant equal to 300. What we want is the most basic angle that gives a cosecant equal to 300 For other angles, we need to consider a range of functions.

Arccot ​​is the inverse of the cotangent function. For example, cot-1(1) means an angle whose cotangent is 1. Cot-11 = 450.

arc seconds

The inverse of the secant is called the arcsecond function. For example, sec-12 means the angle of inclination of which secant is 2. Sec-12 = 600.

Arcsine

The inverse of the sine function is called the arcsine function. For example, sin-1(1/2) = 300.

Equalities arctan

The inverse tangent function is called the equality function arctan. For example, Tan-1(1) = 450

Area below the Curve

The area occupied by a Curve is called the zone that the Curve forms together with X and Y. The area of ​​the function y = f(x) is given by the definite integral inʃB, where A and B are the limits of the function.
Area = aʃb F(x) dx

Area between curves

The area between two curves y = F(x) and Г = Г(x) is determined by the formula,
Area = aʃB |Ф(x) - G(x)|DX, where F(x) and G(x) is the area bounded above and below by the X and Y axes while X= A and x=b, left and right .

Area of ​​a Convex Polygon

If (x1, Y1), (x2, Y2), . , (xn, YN) represent the coordinates convex polygon, then the area of ​​the polygon is determined by the determinant method. When expanded, the determinant looks like this:
1/2[(x1y2) + x2y3+ x3y1+ . xny1)] - .

Area of ​​the ellipse

The area of ​​the ellipse is determined by the formula ∏AB, where A and B are the lengths of the major and minor axis of the ellipse. If the ellipse has its center at (h, k) then
Area = [(x-x)2/A2 + (y-K)2/B2]

Area of ​​an Equilateral Triangle

The area of ​​an equilateral triangle is found by the formula:
A2√3/4, where a = side of an equilateral triangle.

Kite area

The area of ​​the kite is determined by the formula:
½ (Product of diagonals) = ½ d1d2 x.

Area of ​​Parabolic Segment

The area of ​​a parabolic segment is determined by 2/3 of the product's width and height.

Area of ​​a parallelogram

Area of ​​a parallelogram = base x height of the parallelogram.

Area of ​​a rectangle

Area of ​​rectangle = length x width

Area of ​​a regular polygon

Area of ​​a regular polygon = ½ x apothem x perimeter.

Area of ​​a rhombus

The diagonals of a rhombus are perpendicular to each other. Area = ½ x products of diagonals or Area = H x s, where H and s are the height and side of the rhombus.

Area of ​​a circle segment

We all know the area of ​​a circle, and if the area of ​​a segment needs to be found, the formula for the area of ​​a circle segment is:
Area = 1/2r2(θ - sinθ) (radians)

Area of ​​trapezoid

Area of ​​trapezoid = ½ x (sum of non-parallel sides) x = ½ x (B1 + B2) x

Area of ​​a triangle

There are various formulas to calculate the area of ​​a triangle which are as follows.
Area = A = ½ X base x height
A = ½ x AB Deshaies = ½ x BC. e. Sin = i/2 x ka-SinB, where A, B and C are the angles of the triangle respectively.
Given C= A+B+C/2 (semi-perimeter), according to Heron’s formula, A= [C(C-A)(C-B)(C-C)]1/2.
If "P" and "P" are inscribed and circumscribed to the incircle and outercircle of the triangle, then Area (A) = R and b = ABC/4P, a, b and C of the sides of the triangle.
Areas Using Polar Coordinates

When polar coordinates are included in area calculations, the area is determined by the formula:
The area between the graph p = p(θ) and the origin, as well as between the lines θ = α and θ = β is determined by the formula:
Area = ½ αʃβ r2d by θ

Argand plane

The complex plane is called the Argan plane. Basically, the argan plane is used to represent complex numbers graphically. The x-axis is called the real axis and the y-axis is called the imaginary axis.

Complex Number Argument

To describe the angle of inclination or complex number on the argan plane, we use the term argument. The argument of a complex number in radians. The polar form of a complex number is given by p(cosθ + isin codeθ) and the argument for this is given by θ.

Function argument

The expression in which the function operates is called the function argument. Function argument y= √x x.

Vector argument

The magnitude of the angle describing a vector or string in complex analysis is called the argument of the vector.

Average

The simplest medium technique that we use in everyday life.
For example, if there are 4 values, then the arithmetic mean is determined by the following formula:
Arithmetic mean = (A + B + B + C + D)/4

Arithmetic Progression

From the series that there is a difference between its conditions. For example, 1, 3, 5, 7, 9. to infinity. The nth expression of an arithmetic progression is determined by the following formula: tn = A + (H-1)d, where A = 1st quarter, N = number of terms, and D = difference. It is also called sequence arithmetic. The sum of the arithmetic progression is found by the formula: s = n/2 or s = n(A1 + An)/2, where N = number of terms.

Angle lever

One of the rays/lines forming an angle with another is called a bracket angle.

Right triangle hand

Any of the sides of a right triangle is called the arm of a right triangle.

Associative

The operation A + (B + C) = (A + B) + C is called an associative operation. Addition and multiplication are associative, but division and subtraction are not. For example, (4+5)+ 7 = 4 + (5+7)

Asymptote

An asymptote of a Curve or a line that approaches the Curve very closely. There are horizontal and oblique asymptotes, but not vertical asymptotes.

Extended Matrix

The matrix representation of a system of linear equations is called an extended matrix.
For example, 3x - 2y = 1 and 4x + 6 years = 4, then in matrix form 3, 2 and 1 (from the 1st equation) and 4, 6 and 4 (from the 2nd equation) form the elements of the 3x3 matrix, respectively .

Average

On average the same as the arithmetic mean.

Average rate of change

The change in the slope of a line is called the average rate of change of the line. Also, the change in value, quantity divided by time is the Average Rate of Change.

Mean value of function

For the function y =f(x) In the intervals [a,b] average value determined by the formula (1/B-A)ʃBF(x)DX

The X, Y and Z axes are called the coordinate system axes.

Axiom

A statement that is accepted as true without any evidence.

Cylinder axes

A line that passes exactly through the center of the cylinder and also passes through the bases of the cylinder. Simply put, on the line dividing the cylinder into two equal halves vertically.

Reflection axes

The line along which the reflection occurs.

Axis of rotation

The axis along which the axis rotates.

Axes of symmetry

The line along which Geometric figure or the shape is symmetrical.

Axis of symmetry of a parabola

The axis of symmetry of a parabola is the line that passes through the focus and vertex of the parabola.
Topb

Reverse Substitution

Inverse substitution is a method that is used to solve a system of linear equations that has already been modified in a row-echelon form and a lowered row-echelon form. After replacing the equation, the first equation is solved, then the penultimate one, then the next one, and so on.

Base (Geometry)

Bottom part A geometric figure, like a solid object or a triangle, is called the base of the object.

Expression database

Consider an expression of the form AX. Then "a" can be called the base expression axe.

Base of an isosceles triangle

Base isosceles triangle the sides of the triangle are not equal. In other words, it is different than the legs of a triangle.

Trapezoid base

A trapezoid has four sides parallel to each other. Either of the two parallel sides can be considered as the base of a trapezoid.

Triangle base

The base of the triangle is the side on which the height can be drawn. This is the side that is perpendicular to the height.

Bearing

Bearing is a method used to indicate the direction of a line. If there are two points A and B, then a bearing can be said to have θ degrees from point B if the line connecting A and B makes an angle θ with a vertical line drawn through B. The angle is measured clockwise.

Bernoulli tests

In the field of statistics, Bernoulli tests are experiments where the result can be either true or false. In Bernoulli tests, all events must be independent. The binomial probability formula is p (K successes in N trials) = nCrpkqn - K, where,
N= number of samples,
k = number of successes,
N - K = number of failures,
p = probability of success in trials
m = 1 - p, probability of failure in one trial.

Beta (Β β)

The Greek letter is often used as a symbol to represent variables.

Double condition

It is a way of expressing an instruction containing more than one condition, that is, a condition and its converse. These statements are called biconditionals. They are represented by the symbol ⇔. For example, the following statements can be called biconditionals: "this triangle is equilateral" is the same as "all angles of a triangle measure 60º."

A binomial can simply be defined as a polynomial in which there are two terms, but they are not similar terms. For example, 3x - 5z3, 4x - 6y2.

Binomial Coefficients

The coefficients of various expressions in the binomial expansion of Newton's binomial are called binomial coefficients. Mathematically, the binomial coefficient is equal to the number of elements R that can be selected from a set of N elements. They are simply called binomial coefficients because they are coefficients of binomial extended expressions. As a rule, they are presented on the RNS.

Binomial coefficients in Pascal's triangle

Pascal's triangle is an arithmetic triangle used to calculate the binomial coefficients of various numbers. Binomial coefficients (BCs) in Pascal's triangle are called binomial coefficients in Pascal's triangle. Pascal's triangle finds its main application in algebra and probability theory theorem/binomial.

Binomial Probability Formula

The probability of M successes in N trials is called the binomial probability formula. The formula is determined by the formula:
Formula: p(M successes in N trials) = mCnpkqn-K, where,
N = number of trials
M = number of successes
N - m = number of failures
p = probability of success in one trial
question = probability of failure on one trial.

Binom theorem

The theorem is used to extend the powers of the polynomial and equation. It is found by the formula:
(A + B)N = nC0an + nC1an-1B + . +NTN-1abn-1 +NTN.

Boolean Algebra

Boolean algebra deals with logical calculus. Boolean algebra takes only two values ​​in logical analysis, either 1 or zero. Read more about logical occurrences.

Boundary Value Problem

Any differential equation that has a restraining effect on the values ​​of a function (not like derivatives) is called a boundary value problem.

Limited Function

A function that has a limited range. For example, in a set, the top 9 is a limited number and the bottom 2 are a limited number.

Limited Sequence

A sequence that is bordered by an upper and lower boundary. Like a harmonic series, 1, ½, 1/3, ¼, . to infinity is a bounded function, since the function lies between 0 and 1.

Limited set of geometric points

A limited set of geometric points is called a figure or set of points that can be contained within a fixed space or coordinates.

Limited set of numbers

Set of numbers with bottom and upper limit. For example, a limited set of numbers is called.

Boundaries of Integration

For a definite integral, aʃB Ф(Х)DX, A and B are called boundaries or limits of integration. Within the framework of integration, also indicate the limits of integration.

Box

A rectangular parallelepiped is often called a box. The volume of such a rectangular box is determined by the product of length, width and height.

Box with mustache plot

The Boxes and Tanks plot is the beginning of a lesson for beginners to let them understand the basics of data processing. The Whisker Box Chart shows some data rather than full statistics of the recorded data. Five summary number is another name for visual representation and plot.

Box plot

The data that displays the five number of resumes in schematic form is presented as:

Small
1st Quartile
Median
3rd Quartile
Largest

Suspender
Symbolic representation (or), which is used to indicate sets, etc.

The symbol means that the grouping. They work in a similar way to how parentheses do.
Genpsk

Calculus

The branch that deals with integration, differentiation, and various other forms of derivatives.

Numerals

Cardinal numbers indicate the number of elements in infinite or finite.

Cardinality

It is the same as numerals. It should be noted that the cardinality of any infinite set is the same.

Cartesian Coordinates

Cartesian coordinate axes that are used to represent the coordinates of a point. (x,Y) and (X,y,Z) are Cartesian coordinates.

Cartesian planes

The plane formed by the horizontal and vertical axes, like the X and Y axes, is called the Cartesian plane.

Contact network

The curve formed by a hanging wire or ring is called a chain. As a rule, chain is confused with parabola. However, although superficially similar, it is not the same as a parabola. The graph of hyperbolic cosine is called a catenary network.

The cavalier principle.

A way to find the volume of solids using the formula V = BH, where B = cross-sectional area of ​​the base (cylinder, prism) and H = height of the solid.

Central Angle

An angle in a circle with its vertex at the center of the circle.

Centroid

The point of intersection of three medians of a triangle.

Centroid Formula

The centroid of points (x1, Y1, x2, Y2, . xn, yn) is determined by the formula:

(x1 + x2 + x3+ . хп)/п, (У1 + У2 + У3+ . уя)/н

Chevy's theorem

Cev's theorem is a way that relates the relation in which three parallel cevians divide a triangle. If AB, BC and CA are the three sides of the triangle, and AE, BF and CD are the three cevians of the triangle, then by Ceva's theorem, in
(AD/DB)(BE/EU)(MV/PA) = 1.

A line that extends from the vertex of a triangle to the opposite side, like the altitude and median.

Chain Rule

The method of differential calculus is used to find the derivative of a complex function.
(d/DH)F(G(X)) = f"((G(x))G"(x) or (DU/DH) = (di/DU)(DU/DH)

Changing the Basic Formula

A very useful logarithmic formula that is used to express a specific logarithmic function to another base. That's why it's called the formula, change the base.
Changing the Basic Formula: logax = (logbx/logba)

Check the solution

Checking a solution means taking the values ​​of the corresponding variables into an equation and checking if the equation satisfies a given equation or system of equations.

A chord is a line segment connecting two points on a curve. In a circle, the largest chord is the diameter that connects the two ends of the circle.

The locus of all points that are always at a fixed distance from a fixed point.

Circular Cone

Cone with a circular base.
The volume of a circular cone is found by the formula V = 1/3πR2 and

Circular Cylinder

A cylinder with a circle at the base.

Circles

The center of a circle is called a circle.

Circles

A circle that passes through all the vertices of a regular polygon and triangle is called a circle.

There is a circular pattern around the perimeter.

Circumscribable

A drawing is a plan that has circles.

Limited

The figure is limited by a circle.

Circumference

A circle that touches a vertex of a triangle or regular polygon.

Clockwise

The direction of movement of the watch hand..

Closed Interval

A closed interval is one in which both the first and last terms are included in the consideration of the entire set. For example, .

Coefficient

A constant number that is multiplied by variables and powers in algebraic expression. For example, in 234x2yz, 243 is the coefficient.

Coefficient Matrices

The matrix formed by the coefficients of a linear system of equations is called a coefficient matrix

Cofactor

If a determinant is obtained by removing the rows and columns of a matrix in order to solve the equation, it is called cofactors.

Matrix Factor

Matrices with elements from factors, term by term, in a square matrix are called a cofactor matrix.

Cofunction Personality

Cofunction IDs that show the relationship between trigonometric functions such as sine, cosine, cotangent.

Coincidence

If two figures overlap each other, they are said to coincide. In other words, the pattern matches when all the points match.

Collinear

Two points are called collinear if they lie on the same line.

Matrix columns

The vertical set of numbers in a matrix is ​​called a column of the matrix.

Combination

Selecting items from a group of items. The order does not matter when selecting an object.

Combination Formula

A formula that is used to determine the number of possible combinations of P objects from a set N of objects. The formula assumes binomial coefficients and is defined as:
RNS. It reads "N choose p"

Combinatorics

The branch that studies the permutations and combinations of objects and materials.

Decimal Logarithm

A logarithm with base 10 is called a decimal logarithm.

Commutative

An operation is called commutative if x ø Г = Г * x, for all values ​​of X and Y. Addition and multiplication are commutative operations. For example, 4 + 5 = 5 + 4 or 6 x 5 = 5 x 6. Division and subtraction are not commutative.

Matrix Compatibility

Two matrices are said to be compatible for multiplication if the number of columns of the 1st matrix is ​​equal to the number of rows of the other.

Complement angle

The complement of an angle of 75º is said to be 90º 75º = 15º.

Complementary events

The set of all outcomes of an event that are not included in the event. The composition of the set is written as AC. The formula is defined as: P(AC) = 1 - P(A) or p (Not A) = 1 - P(A).

Complete the set

Elements of a given set that are not contained in this set.

Additional Angles

If the sum of two angles is 90º, then they are said to be complementary angles. For example, 30º and 60º are complementary, and their sum is 90º.

Composite Number

Itself is a positive integer whose factors are the numbers 1 and the numbers. For example, 4, 6, 9, 12, etc. 1-This is not a composite number.

Fraction Mixture

Fraction composition is a fraction that has at least one fraction term in the numerator and denominator.

Compound Inequality

When two or more than two inequalities are solved together it is known as a compound inequality.

Compound interest

When calculating compound interest, the amount that was earned as interest on a certain amount/principal is added to the original participant, and from this interest is calculated on the new principal. Thus, the interest is not only calculated on the original balance, but the balance or principal received after the addition.

Concave

A concave-shaped figure or body having a surface that curves inward or bulges outward. It is also known as non-convex. Concave concave down or up, other concave shapes.

Concentric

Geometric shapes that are similar in shape and have a common center. Generally, the term is used for concentric concentric circles.

Simultaneously

If two or more than two lines or curves intersect at one point, then they are said to be simultaneous at that moment.

Conditional Equation

An equation that is true for some values ​​of the variables and false for other values ​​of the variables. An equation has certain conditions imposed on it that satisfy only certain values ​​of the variables.

Because-1x

Reverse cos functions read as because the inverse is x. For example, that -1½ = 60º.

Cot-1x

Buy a crib-1x, we mean the angle whose cotangent is x. For example, when we are asked to find the smallest angle whose cotangent is 1? The answer is 45º. Thus, crib-11 = 45º.

A cube is a three-dimensional figure bounded by six equal sides. The volume of the Cube is given in L3, where L is the side of the Cube.

Cube Root

The cube root is a number denoted by x⅓ such that B3 = x for example, (64)⅓ = 4.

Cubic Polynomial

A polynomial of degree 3 is called a cubic polynomial. For example, x3 + 2x2 + x.

Cuboid

A parallelepiped is a three-dimensional box that has length, width and height. It is also called a cuboid.
TopD

Moivre's theorem is

De Moiver's theorem is a formula that is widely used in the complex number system to calculate powers and roots of complex numbers. It is found by the formula:

[р(cosnθ + isin codθ)]н = рН(cosnθ + isinnθ).

Decagon

The 10 square is called a decagon.

Deciles

According to statistics, deciles are any of nine values, dividing the data into 10 equal parts. The first decile cuts off at the low 10% of the data, which is called the 10th percentile. The 5th decile cuts off the low 50% of the data, which is called the 50th percentile or 2nd quartile and median. The 9th decile cuts off the low 90% of the data, the 90th percentile.

Decreased Functions

A function whose value continuously decreases as you move from left to right on its graph is called a decreasing function. A line with a negative slope is a great example of a decreasing function, where the value of the function decreases as we move to the x-axis. If a decreasing function is differentiable, then its derivative at all points (where the function decreases) will be negative.

Definite Integral

Inherent, which is calculated on the interval. This is given by ʃBF(x)DX. Here the interval is [a, b].

Degenerate Conic Sections

If a double cone is cut by a plane passing through the vertex of the plane, then it is called a degenerate conic section. It has general equations of the form:

Ax2 + Bxy Po + Cy2 + Dx + Eu + Ф = 0

Degrees (measurement angle)

A degree is a measure of the slope or angle, lines or planes subtended. The degree is indicated by the symbol "°".

Polynomial degree

The power of the highest term in an algebraic expression is called the degree of a polynomial. In the expression 2x5 + 3y4 + 5x3, the degree of the polynomial is 5.

Degree term

In 5y7, the degree term is 7, in 5x24y3, the term term is the sum of the exponents 5x and 4d, which means 5.

Operator-Del -

The del operator is denoted by the symbol ∂(x, y, Z)/∂x. Operator division ∇ = (∂/∂х, ∂/∂Y) or (∂/∂х, ∂/∂г, ∂/∂з)

Remote Areas

The remote neighborhood set is defined as the set (x: 0
Delta (Δδ)

Greek letter representing the principal discriminant of a quadratic equation.

Denominator

The bottom part of the fraction is called the denominator. As a fraction (4/5), 5-denominator.

Dependent Variable

Consider the expressions y = 2x + 3, where x is the independent variable and Y is the dependent variable. This general concept to plot a graph by taking the independent variable on the X-axis and the dependent variable on the Y-axis.

Derivatives

The slope of a tangent to a function is called the derivative of the function. This is a graphical interpretation of the derivative. As an operation of differentiation, consider F(x) = x2, then its derivative F"(x) = 2x.

Descartes' rule of signs

A method for determining the maximum number of positive zeros of a polynomial. According to this rule, the number of changes in the sign of an algebraic expression gives the number of roots of the expression.

Determinant

Determinants are mathematical objects that are very useful in determining the solution to a system of linear equations.

Matrix Diagonal

A square matrix that has zeros everywhere except the main diagonal.

Diagonals of a polygon

A line segment connecting non-adjacent vertices of a diagonal. If a polygon has n sides, then the number of diagonals is determined by the formula:
H(H-3)/2 diagonals.

Diameter

The longest chord of a circle is called the diameter. It can also be defined as a line segment passing through the center of a circle and touching both ends of the circle.

Diametrically Opposite

Two points are directly opposite each other in a circle.

Difference

The result of subtracting two numbers is called the difference.

Differentiability

A curve that is continuous at all points of its domain is called a differentiable function. In other words, if there is a derivative along a curve at all points of the variable domains, it is said to be differentiable.

Differential

Tiny and infinitesimal change in the value of a variable.

Differential equation

Equation with functions and derivatives. For example, (DU/DH)2 = g

Differentiation

By performing the process of finding the derivative.

Any of the nine digit numbers, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Dihedral angle

The angle formed by the intersection of two planes.

Dilatation

Dilation refers to the expansion of a geometric figure by transformation.

Dilatation of a geometric figure

A transformation in which all distances increase according to some common factor. The scores ranged from a common fixed point p.

Dilatation Chart

In graphical dilatation, the x-coordinates and y-coordinates are increased by some common factor. The transformation coefficient of the graph being done must be greater than 1. If the coefficient is less than 1, it is called compression.

Dimensions

The sides of a geometric figure are often called dimensions.

Matrix dimensions

The number of rows and columns of a matrix is ​​called Matrix Size. For example, if a matrix has 2 rows and 3 columns, then its dimensions will be 2x3 (read as two or three).

Direct Proportions

When one of the variables is a constant to several others, this is called the direct variant. For example, Y = KX driver (here Y and X are variable quantities, and K is a constant coefficient).

Ellipse guides

Two parallel lines on the outside of the ellipse, located perpendicular to the main axis.
Tope

E is a transcendental number that has a value approximately equal to 2.718. It is often used when working with logarithms and exponential function.

Eccentricity

A number that determines the shape of the Curve. It is represented by the small letter "E" (this E is in no way related to the exponential E = 2.718). In a conic section, eccentricity curves are the ratio between the distance from the center to the focus, and the horizontal and vertical distances from the center to the apex.

Stepped matrix view

The echelon matrix is ​​used to solve a system of linear equations.

Polyhedron Edge

One of the line segments that together make up the faces of a polyhedron.

Matrix element

The numbers inside a matrix in the form of rows and columns are called a matrix element.

Set element

Any point, line, letter, number, etc. contained in a set is called a set element.

Blank Set

A set that does not contain any element. The empty set is denoted by () or Ø.

Properties of equality equation

Equality properties of algebra that are used to solve algebraic equations. The definitions of these equality properties are as follows:
x = Y means that x is equal to Y and Y ≠ x means that Y is not equal to x. The operations of addition, subtraction, multiplication and division are all true for the equality property of an equation.
Reflexive properties - x = x;
Symmetrical property - if x = y, then y = x;
Transitivity - if X = Y and Y = Z, then x = z

Equilateral triangle

An equilateral triangle has three equal sides and each angle measures 60º.

Equivalence Relationship

Any equation that is reflexive, symmetric and transitive.

Equivalent systems of equations

Two sets of equations that have the same solutions.

Significant Discontinuities

These are the types of discontinuities in a graph that cannot be removed simply by adding a period. There is a significant discontinuity at the point; the limit of the function does not exist.

Euclidean geometry

The geometric study of lines, points, angles, quadrilaterals, axioms, theorems and other branches of geometry is called Euclidean geometry. Euclidean geometry named after Euclid, one of the greatest Greek mathematicians and known as the "father of geometry". Read more about famous mathematicians.

Euler's formula

Euler's formula gives EIπ + 1= 1. This is a widely used formula in complex quantity analysis.

Euler's Formula in Polyhedron

For any polyhedron, the following relation is valid:
[Number of faces(n)] - [number of vertices(V)] - [Number of edges(E)] = 2.
This formula is true for all convex and concave polyhedra.

Even Function

A function whose graph is symmetrical about the Y axis. In addition, Ф(-Х) = F(х).

Even Quantity

The set of all integers that are divisible by 2. E= (0, 2, 4, 6, 8.)

Explicit Differentiation

The derivative of an explicit function is called explicit differentiation. For example, Y = x3 + 2x2 - x3. Differentiating this gives,
y"= 3x2 + 4x - 3.

Explicit Functions

In an explicit function, the dependent variable can be expressed entirely in terms of the independent variables. For example, Y= 5x2 - 6x.

Exhibitor Rules

The exponential rules are as follows.

Serial number
Exponential Formula
1
anam = K+M
2
(a. b)N = c. billion
3
A0 = 1
4
(i)n = anm
5
i/N = N√AM
6
a-m = 1/A-M
7
(I/K)= A(M-N)

Extreme Cost Theorem

According to this theorem, there is always at least one maximum and one minimum for any continuous function on a closed interval.

Extreme Polynomial Values

The graph of a polynomial of degree N has no more than N-1 extreme values ​​(maxima or minima)
Topfa

Face of the Polyhedron

The polygonal outer boundary of a solid object, having no curved surfaces.

Integer factor

If a given integer is divisible by another number, the resultant is called the factor of the integer. For example: 2, 4, 8, 16, etc. are factors of 32.

Polynomial coefficient

If the polynomial P(X) is completely divided by the polynomial P(X) by Q(x), then Q(x) is called the coefficient of the polynomial. For example: P(X)= x2+6x+8, and Q(x)=x+4 then P(x)/G(X)= X+2. M(x)=x+4-coefficient.

Theorem factor

When x-a is the coefficient of P(X), the value of x B P(X) is replaced, then if the resulting value is 0, then such a theorem is called the factor theorem. For example: P(x)= x2+6x+24. M(X)= X-(-4). If x is replaced, then -4, then p(x)= 0.

Factorial

The product of an integer with all smaller numbers in a row is called the factorial. She is represented as "N!" For example: 5! = 5*4*3*2*1= 120.

Factoring Rules

These are the formulas that govern the factorization of a polynomial. For example,
x2-(A+B)x +AB= (x-a)(x-b).
x2+2(A)X+A2=(x+a)2
x2-2(A)X +A2=(x-a)2
Read more about grouping coefficient.

Fibonacci series

It is a series of numbers where the next number is found by adding the previous two numbers in the series. The first two digits of the series are 0 and 1. The series is 0,1,2,3,5,8.

Final

This term is used to describe a group in which all elements can be counted using natural numbers.

First Derivative

Function F(A), which adjusts the slope of the Curve to any given point, or the slope of a line drawn tangent to the Curve from this point on the plane is called the first derivative. It is represented as F". For F(x)= 5x2. F"(x)=10x will be the slope of the Curve.

First derivative test

A technique used to determine the inflection point potential. (minimum, maximum, or none)

First order differential equation

It is also known as the reflection axis. This is a line that divides a plane or geometric figure into two parts, which are mirror image each other.

Gender Function (Greatest Integer Function)

This is the function f(x), which is responsible for finding the largest integer less than the actual value of F(x). For example: P(X)= 5. 5, here the largest integer is less than 5. 5 is 5. The function that gives F(x)=5 becomes the floor function.

Ellipse focuses

They are fixed two points inside the ellipse such that the vertical Curve is determined by the formula L1 + A2 = 2a and the horizontal Curve in accordance with the equation L1 + A2 = 2B, where L is the distance between the focal point and the curve, a is the horizontal radius and the vertical radius b.

Hyperbole tricks

They fix two points inside the curve of the hyperbola, such that the determinant A1-A2 is always constant. L1 and L2 are the distances between point p (which is a curve) and the corresponding direction of the Curve.

Conic section curves are adjusted by distance from a special point called the focus.

Focus parabola

In parabolas, the distance from a point p on a curve and an arbitrary point inside the parabola is equal to the distance between the same point p and the directrix of the curve. Such an arbitrary point is called the focus of the parabola.

Foil method

Foil is an abbreviation of first external internal past. This is the method by which binomials are multiplied. Multiplication order
First members of Binomials
External conditions Binom
Inner circle binomials
External conditions of Binoma.
For example: (a+b)(A-B)= A. A+A. (-B)+B. A + B. (-b)

Formula

The relationships between different variables (sometimes expressed as an equation) are depicted using symbols. For example: A+B=7

Fractal

When every part of a shape is similar to every other part of another shape, the shape is called a fractal.

Fraction

This is the relationship between two numbers. For example: 9/11.

Faction Rules

Algebra rules are used to unite the different factions.

Fractional Equations

An expression in the form A/B on both sides of the equal sign is called a fractional equation. For example: x/6= 4/3.

Activities Functions

Various operations, such as addition, subtraction, multiplication, division and composition, which have a combined effect on various functions. For example: F(A/B) = F(A)/F(b).

Fundamental theorem of algebra

Each polynomial is characterized by one variable, having complex coefficients, will have at least one root, which also complex nature.

Fundamental Theorem of Arithmetic

The statement that the factors of a prime number are always distinct and unequal is a fundamental theorem of arithmetic.

Fundamental Theorem of Calculus

Differentiation and integration are two of the most basic operations in calculus. The theorem that establishes the connection between them is called the fundamental theorem of calculus.
Bargain

Jordan-Gauss Elimination

Method for solving a system of linear equations. In this process, the augmented form of the system matrix is ​​reduced into the form of an echelon series using successive operations.

Gauss method

Method for solving a system of linear equations. In the Gaussian elimination method, the augmented form of the matrix is ​​reduced to a series of step forms, and then the system is solved by inverse substitution.

Gaussian Integer

Gaussian integers in complex numbers, presented in + Bi. For example, 3 + 2i, 5i and 6i + 5 are called Gaussian integers.

The largest integer that divides a specified set of digits. Its full form is called greatest common divisor. For example, RGS volumes of 20, 30, and 60 are 10.

General view of the line equation

John of Seville (1140), Robert of Chester (1145) and Gerard of Cremona (1150) general view the equation of a line is the equation
Ax + by + c = 0, where A, B and C are integers.

Geometric figure

A geometric figure is a set of points on a plane or space that leads to the formation of a figure..

Geometric Mean

Geometric mean is a method of finding the mean using a specific set of numbers. For example, if there are numbers A1, A2, A3, . AN, then multiply the numbers and take the root of the N-product.

Geometric mean = (A1, A2, A3, . , c)½

Geometric progression

Geometric progression is a sequence whose conditions are in constant relation to previous conditions. For example, 2, 4, 8, 16, 32, . , 28 conditions geometric progression. Here the overall coefficient is 2. (like 4/2 = 8/4 = 16/8.)

Geometric Series

A geometric series is a series of successive ones whose terms are in constant proportion. Example of geometric progression 2, 4, 8, 16, 32, .

Geometry

The study of geometric shapes in two and three dimensions is called geometry.

Largest lower bound

The greatest of all lower bounds on a set of numbers is called GLB or greatest lower bound. For example, in the set , the GLB is 2.

Gliding Reflections

Transformation, in which the drawing must go through a combination of translation and reflection stages.

Global Maximum

The highest point on the graph of a function or relation (in the domain of the function). First and second derivative tests are used to find the maximum value of a function. It is also called the global maximum, absolute maximum, and relative maximum.

Global Minimum

The lowest point on the graph of a function or relationship. First and second derivative tests are used to find the minimum value of a function. It is also called the global minimum, absolute minimum or global minimum.

Golden mean

The ratio (1 + √5)/2 ≈ 1. 61803 is called the golden mean. Unique property The golden mean is that the mutual golden mean is about 0.61803. Therefore, the golden mean is one plus its reciprocal.

Golden Rectangle

If the ratio of length and width of a rectangle is equal to the golden mean, then the rectangle is called a golden rectangle. It is believed that this rectangle is the most pleasing to the eye.

Golden Spiral

Spirals that can be drawn inside the golden rectangle.

The number 10100 is called a googol.

Googolplex

Googolplex can be written as 10100100.

Graph of an equation or inequality

A graph produced by plotting all the points in a coordinate system.

Graphic Methods

Using graphical methods to solve mathematical problems.

Big Circle

A circle drawn on the surface of a sphere that shares a common center with a circle.

Greatest Entire Function

The largest number of functions of any number (say x) is an integer less than or equal to x." The largest integer function is represented as [x]. For example, = 3 and [-2.5] = 3
Pacific Fleet

Half corner ID

Trigonometry identities that are used to calculate the value of sine, cosine, tangent, etc. from half a given angle.
Trigonometric identities

Additive. The word comes from the Latin additio - “addition”, “adding”.

Axiom. The term was first found in Aristotle and passed into mathematics from philosophers ancient Greece. Translated from Greek, the word means “dignity”, “respect”, “authority”. Originally the term had the meaning of “self-evident truth.”
In the modern understanding, an axiom is a statement of some theory, accepted when constructing this theory without proof, i.e. accepted as the initial, starting point for proving other provisions of this theory (theorems). Axioms are also called postulates.

Algebra. Mathematical science, the object of study of which is algebraic systems, for example groups, rings, fields, etc. A separate branch of algebra is elementary algebra.
The first algebra textbook - " Brief book on the calculation of al-Jabr and al-Muqabala" was written in 825 by the Arab scientist al-Khorezmi. The word al-jabr meant the operation of transferring subtracted from one part to another and its literal meaning is “replenishment”. This term became the name science. In Europe, this name was used already at the very beginning of the 13th century, but Newton called algebra “General Arithmetic” (1707). special meaning in the history of mathematics as a guide by which for a long time All of Europe studied. It was under the influence of Arab mathematics that algebra was formed as a study of solving equations.

Algorithm. In the 9th century. al-Khwarizmi outlined the positional system in his essay “On the Indian Number”. The Latin translation of this work began with the words: “Dixit Algorithmi,” said al-Khwarizmi.” This is where the term “algorithm” (“algorithm”) came from. medieval Europe the word meant the entire system of decimal positional arithmetic.
Modern concept The algorithm was established in the mid-30s of the XX century. in the works of Gödel, Church, Turing, Post, A.A. Markova. An algorithm is an exact formal prescription that unambiguously defines the content and sequence of operations that transform a given set of initial data into the desired result.
IN primary school The simplest algorithms are the rules by which addition, subtraction, multiplication, and division are performed.

Analysis. A logical technique or research method consisting in the fact that the subject under consideration is mentally or practically divided into its component parts (signs, properties, relationships). Each of these parts is studied separately, so that the parts identified during the analysis can then be combined using another logical technique - synthesis.
The concepts of analysis and synthesis were known back in ancient Greece. Translated from ancient Greek, analysis means “decision”, “resolution”.
In elementary school, we very often use analysis to solve a variety of problems.

Analogy. Similarity, similarity of objects or phenomena in some properties, characteristics, relationships, and these objects themselves, generally speaking, are different. In mathematics, inference is often considered by analogy, the similarity of individual properties (features) when comparing two sets (figures, relationships, objects, etc.).
The analogy is very accessible and simple as a method of reasoning, but it first of all allows you to put forward a hypothesis, which then needs to be strictly proven.

Aporia. A false statement that ancient Greek scientists sometimes resorted to in their reasoning. The aporia of the ancient Greek philosopher Zeno (V-IV centuries BC) “Achilles and the tortoise” is well known. She claims that fleet-footed Achilles will never catch up with the tortoise, since when Achilles reaches the place where the tortoise was, it will move forward some distance; when Achilles reaches the second location of the turtle, it will again advance some distance, even if less than before, etc. Thus, Achilles will never catch up with the tortoise.

Arabic numerals. A collective term for ten mathematical symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, which allow you to write any number in the decimal positional notation system. It would be more correct to call Arabic numerals Indo-Arabic, because came to Europe from India through the Arabs around the 11th century.

Arithmetic. The concept translated from Greek means number. Because The Greeks considered only whole numbers, large units, to be numbers, then their arithmetic was the science of whole numbers, the properties of numbers. The art of counting and the rules of operations with numbers belonged to “logistics” - a lower-order science. The word entered the Russian language in the 16th century. Almost all mathematical books of that time began the same way: “The book is arithmetic in Greek, algorithm in German, and numerical counting wisdom in Russian.”
In the modern understanding, arithmetic is the science of numbers and operations on them. Arithmetic is often called theoretical arithmetic or number theory. A clear distinction cannot be made between algebra and arithmetic.

Arithmomancy. Religious and mystical idea of ​​the magical role of numbers, fortune telling and fortune telling using numbers. The Pythagoreans (members of the Pythagorean school) especially believed in the power of arithmomancy.

Angle bisector. A ray emanating from the top of a corner and dividing it in half.

Axiom- a statement accepted without evidence.

Algebraic expression- a certain number of numbers, designated by letters or numbers and connected using the operations of addition, subtraction, multiplication, division, exponentiation and root extraction.

abcissa(French word). One of the Cartesian coordinate points. Is the first. Typically indicated by the symbol "X". First used by G. Leibniz in 1675 (German scientist).

Additivity. Some property of quantities. It says the following: the value of a certain quantity corresponding to a full-fledged object is equal to the sum of the values ​​of such a quantity that correspond to its parts in any division of the full-fledged object into parts.

Adjunct. Completely corresponds to algebraic complement.

Axonometry. One of the ways to depict spatial figures on a plane.

Algebra. The part of mathematics that studies problems and solutions of algebraic equations. The term was first seen in the 11th century. Used Muhammeda ben-Musa al-Khwarizmi (mathematician and astronomer).

Argument (functions). A variable quantity (independent) with the help of which the value of a function is determined.

Arithmetic. The science that studies operations with numbers. Originated in Babylon, India, China, Egypt.

Asymmetry. Absence or violation of symmetry (reverse symmetry).

Infinitely large quantity- greater than any predetermined number.

Infinitesimal- less than any finite one.

Billion. One thousand million (one followed by nine zeros).

Bisector. A ray that starts at the vertex of an angle (divides the angle into two parts).

Vector. A directed segment is a straight line. One end is the beginning of the vector; the other is the end of the vector. The term was first used by W. Hamilton (Irish scientist).

Vertical angles. A pair of angles that have a common vertex (formed by the intersection of two straight lines in such a way that the side of one angle is a direct continuation of the second).

Vector- a quantity characterized not only by its numerical value, but also by its direction.

Schedule- a drawing that clearly depicts the dependence of one quantity on another, a line that gives a visual representation of the nature of the change in a function.

Hexahedron. Hexagon. The term was first used by Pappa of Alexandria (an ancient Greek scholar).

Geometry. The part of mathematics that studies spatial shapes and relationships. The term was first used in Babylon/Egypt (5th century BC).

Hyperbola. An open curve (consists of two unlimited branches). The term appeared thanks to Apollonius of Perm (ancient Greek scientist).

Hypocycloid. This is the curve that a point on a circle describes.

Homothety. The arrangement of figures (similar) among themselves, in which the straight lines connecting the points of these figures intersect at the same point (this is called the center of homothety).

Degree. Unit of measurement for a plane angle. Equal to 1/90 of a right angle. Measuring angles in degrees began more than 3 centuries ago. Such measurements were first used in Babylon.

Deduction. Form of thinking. With its help, any statement is deduced logically (based on the rules of the modern science of “logic”).

Diagonal. A straight line segment that connects the vertices of a triangle (they do not lie on the same side). Euclid (3rd century BC) first used the term.

Discriminant. An expression made up of quantities that define a function.

Fraction- a number made up of an integer number of fractions of a unit. Expressed as the ratio of two integers m/n, where m is the numerator, showing how many parts of a unit are contained in the fraction, and n is the denominator, showing how many parts the unit is divided into.

Denominator. Numbers that make up a fraction.

Golden ratio- dividing a segment into two parts so that the larger part is related to the smaller one in the same way as the entire segment is related to the larger part. Approximately equal to 1.618. A criterion of beauty, used in architecture, etc. The term was introduced by Leonardo da Vinci.

Index. Alphabetic or numeric index. With its help it is supplied mathematical expressions(this is done in order to distinguish from each other).

Induction. Method for proving a mathematical equation.

Integral. Basic concept of mathematical analysis. It arose due to the need to measure volumes and areas.

Irrational number. A number that is not rational.

Leg. One of the sides of a right triangle that is adjacent to a right angle.

Square. Regular quadrilateral (or rhombus). Each corner of a square is straight. All angles in a square are equal (90 degrees).

Mathematical constant. A quantity that never changes in its meaning. A constant is the opposite number for a variable.

Cone. A body that is bounded by a single cavity by a conical surface. It intersects the plane (the plane is perpendicular to its axis).

Cosine. It is one of the trigonometric functions. The notation in mathematics/higher mathematics is cos.

Root of the equation- solution, the value of the unknown, found through known coefficients.

- “review, review, view”- constant value.

Coordinates- numbers that determine the position of a point on a plane, surface or in space.

Logarithm. Exponent "m". It must be raised to the power "a" in order to obtain a certain number NT. The logarithm was first proposed by J. Napier.

Line- the common part of two adjacent surface areas.

Maximum. The greatest value of the function.

Scale. The relationship of two linear dimensions to each other. Used in many modern industries. The main ones are cartography and geodesy.

Matrix. Rectangular table. Formed using a set of numbers (defined). Includes columns and rows (matrix structure). The term “matrix” first appeared from the scientist J. Sylvester.

Median. A segment that connects the vertex of a triangle and its midpoint on the opposite side.

Minimum. The smallest value of the function.

Polygon. Geometric figure. Definition: closed polyline.

Module. Absolute value (of a real number).

A bunch of- a set of elements united according to some characteristic.

Norm. The absolute value of a number.

Inequality- two numbers or expressions connected by (greater than) or (less than) signs.

Oval. A convex, closed figure (flat).

Circle. Numerous points located on a plane.

Ordinate. One of the Cartesian coordinates. It is usually designated as the second one.

Octahedron. Geometric figure. One of the five polyhedra (regular). The octahedron includes 8 faces (regular), 6 vertices and 12 edges.

Parallelepiped. Prism. The base is a parallelogram or a polyhedron (equivalent concepts). Has 6 edges. Each face is a parallelogram.

Parallelogram. Quadrangle. Its opposite sides are parallel (in pairs). At the moment there are 2 special cases of parallelogram: rhombus and square. The main property of this geometric figure:
Opposite sides are equal;
Opposite angles are equal.

Perimeter. The sum of all sides of a geometric figure. It was first discovered by Archimedes and Heron (ancient Greek scientists).

Perpendicular. A straight line that intersects a plane (any plane) at a right angle.

Pyramid. Polyhedron. Its base is a polygon. Any other face is a triangle (these faces have a common vertex). At this point the pyramids may be various types: triangular, quadrangular, and so on (they are distinguished by determining the number of angles).

Planimetry. One of the most important parts of elementary (simple) geometry. Planimetry studies the properties of figures that are on a plane. The term was first coined by Euclid (an ancient Greek scientist).

Plus. A sign that denotes a mathematical operation - addition. In addition, the plus symbol denotes positive numbers. The sign was first introduced by J. Widman (the famous Czech scientist).

Limit. Basic concept of mathematics. Denotes: a variable quantity approaches indefinitely constant value(certain). The term was first used by the famous scientist Newton.

Prism. Polyhedron. The first 2 faces are equal triangles (these are the bases of the prism). The rest is the side edges.

Projection. One of the ways to depict spatial and plane figures.

Variable- a quantity whose numerical value changes according to a certain, known or unknown law.

Plane- the simplest surface. Any straight line connecting two of her points belongs entirely to her.

Straight- a set of points common to two intersecting planes.

Percent- hundredth part of a number.

Radian. Unit for measuring angles.

Rhombus. Parallelogram. All sides of this figure are equal. A rhombus with right angles is called a square.

Segment. Part of a circle (it is limited by a chord that connects the ends of the arc).

Secant. Trigonometric function. Notation in Mathematics/Higher Mathematics - sec.

Sector. Part of a circle. Limited by a circle + two radii (connects the ends of one arc to the center of the circle).

Symmetry- correspondence.

Sinus. Trigonometric function. The notation in mathematics/higher mathematics is sin.

Stereometry. Part of elementary geometry. Engaged in the study of full-fledged spatial figures.

Tangent. Trigonometric function. The notation in mathematics/higher mathematics is tg.

Tetrahedron. Polyhedron, includes 4 triangular faces. Each vertex has 3 faces (converging at the vertices). A tetrahedron has 4 faces + 6 edges + 4 vertices.

Dot. Does not have a definite and final concept. Any point is designated using the letters A, B, C.

Triangle. Polygon (simple). Includes 3 tops + 3 sides;

Theorem- a statement that needs to be proven based on axioms and previously proven theorems.

Identity- an equality that is valid for all values ​​of the coefficients included in it.

Topology- a branch of mathematics that studies the properties of figures that do not change under any deformation, without tearing or gluing.

An equation is a mathematical representation of the problem of finding the values ​​of unknowns for which the values ​​of two given functions are equal.

Corner. Geometric figure (flat). It is formed by two rays that come out from one point (the points are the vertices of the angle).

Factorial- the product of natural numbers from 1 to any given natural number n. Denoted by n!. Factorial of zero oh! = 1.

Formula- a combination of mathematical symbols expressing a sentence.

Function- a numerical relationship between elements of two sets, in which one element of one set corresponds to a certain element of another set. Can be specified by a formula or graph.

Chord. A segment that connects 2 points on a circle.

Numbers- signs to indicate numbers.

Center. The middle of something (for example: a circle).

Cylinder. A body that is limited by a cylindrical surface + parallel planes (two). For the first time, the concept of “cylinder” could be found in Euclid and Aristarchus.

Compass. A special device designed to draw arcs, linear measurements and circles.

Numerator. A specific number used to form a fraction. The term was first used by Maximus Planuda (Byzantine scientist).

Number- one of the basic concepts of mathematics, which arose in connection with the calculation of individual objects.

Ball. Geometric body. It is the total set of all points in a certain space.

Exhibitor. Is the same as the exponential function. The term was first introduced by G. Leibniz (German scientist).

Ellipse. Oval curve. This term was first introduced by Apollonius of Perga (ancient Greek scientist).