# Math glossary Absolute value - the distance of a number from 0, always a positive number, represented by |□| Abstract - applying [ideas](values.md) of one domain across to other domains Acute - an angle that's less than 90 degrees Acute triangle - a triangle with less than 90 degrees on all 3 sides Addition - aka putting together, combining grouped values together, is commutative Affine geometry - the only Euclidean geometry left after forgetting distance and angle Algebraic - applying algebra to other domains (e.g., algebraic geometry) Analysis or Analytic - [logically](logic.md) comparing and contrasting values with more logic or math, often by factoring and composing/decomposing to find patterns, contrast to synthetic Angle - a part-circle relationship between geometric elements, represented in degrees Applied mathematics - a branch of mathematics that makes math useful Area - the measured interior of a 2-dimensional shape or the exterior of a 3-dimensional shape, contrast to perimeter Arithmetic - the combined domains of addition, subtraction, division, and multiplication operations Arithmetical - applying arithmetic to other domains (e.g., arithmetic geometry) Asymptotic or Asymptote - describing something that limits something else Base - the counting basis before the increment increases, with our standard numbers being base-10 and [computer math](logic.md) being base-2 (e.g., a base-3 number system would count as 1, 2, 3, 11, 12, 13, 21, etc.) Cardinality - the number of elements in a set Cartesian coordinates - a system that precisely represents 2-dimensional information with two fixed perpendicular lines and signed distances at even intervals, named after its inventory René Descartes (who also developed Enlightenment-era [philosophy](philosophy.md)) Circle - a 1-sided 2-dimensional shape where the distance is the same from the center Circumference - the perimeter of a circle Classical - a math discipline that uses Euclidean space and conventional perspectives of number theory, tends to be the most useful for practical tasks Combinatorial or Combinatorics - the study of various ways to count permutations and combinations of objects beyond addition or multiplication Commutative property - an operation that can rearrange the operands and come to the same answer (e.g., 4 + 3 = 3 + 4), contrast to non-commutative Complex - deals with imaginary numbers as well as real numbers Composing - combining multiple smaller elements to make larger math elements, opposite of decomposing Computable or Computational - applies to [computer-based math](math-cs.md) Connected sum - in topology, the sum of two manifolds Constructive - based on [the philosophy of constructivism](glossary-philosophy.md), where a thing has to be assembled from logic instead of being proven simply by observation Convergent series - a sum of an infinite series of numbers Correlant - two values that are correlated Cube - a 6-sided 3-dimensional shape composed of 6 squares Curve - a line that moves in at least 1 additional dimension Data - information, plural of datum Decompose - splitting a larger element into smaller elements, opposite of composing Decrement - a fixed amount that gets reduced, opposite of increment Degree - the rotated part-circle distance between two points or lines, with 360 being a full circle, represented as ° Denominator - the bottom part of a fraction that denominates the numerator Diameter - the length of a line segment with ends on the circumference that passes through the center of a circle or sphere Differential - tracks quantities of things changing Dimension - aka space, a measurable range that can be geometrically defined, can be Euclidean or non-Euclidean Discrete - counting-based, instead of continuous (measuring-based) Distributive property - the qualities of being able to distribute values [e.g., a (b + c) = ab + ac] Dividend - the number that's getting divided in a division problem Division - separating out values from a dividend into a divisor's number of equally-sized components (e.g., 15 / 3 is 3 values of 5 each, or 5), results in a quotient Divisor - the number of equal components to split a dividend in a division problem Edge - a line that represents part of a shape Element - something in math that's clearly defined (e.g., 2, *i*, f(x)) Elementary - basic or simple Equal - aka equality or equivalent, the state of two things being the same in some mathematical way Equilateral - a shape where all the edges have the same lateral angle Equation - a mathematical formula that shows whether two expressions are equal Euclidean space - the realm of space that inhabits our 3 dimensions, and we call "reality", named after Euclid's proofs, contrasts with non-Euclidean space Evaluate - to parse out the math problem into something else (e.g., 3 + 3 = x becomes x = 6) Exponent - a number multiplied by itself, represented by superscript (e.g., 3^2^), contrast to square root Exterior - where the surface area is the same between multiple things Expression - a logical mathematical statement with at least 2 numbers or variables and at least one operation Extremal - how big or small things can be Face - the side of a shape Factor - aka factorize, to break apart the components that make a larger value or formula [e.g., 2x + 6y = 2 (x + 3y)] Fermi problem - aka from-the-hip guess, a math problem that requires intuitively estimating real-world math Field theory - performing arithmetic on rational and real numbers Finite - only as a limited number of possible things, instead of infinite Forget - to ignore for the sake of finding an answer Formula - a group of operations Fraction - a representation of unresolved division that indicates a part of another value, has a numerator and denominator Function - a clear pattern that can be represented by a formula Game theory - mathematical models of strategic interactions, most notably [decisions](people-decisions.md) based on [understood](understanding.md) and [imagined](imagination.md) circumstances Galois theory - a connection between field theory and group theory Geometry - a branch of mathematics dealing with shapes Geometric - applying geometry to other domains (e.g., geometric algebra) Graph theory - the study of networks of lines and vertices Group or Group Theory - a domain of mathematics that involves conceptually putting things together Higher or Derived - a middle-point on the way to "abstract" Increment - a fixed amount that gets increased, opposite of decrement Infinitesimals - numbers so tiny that they're closer to 0 than to any real number Integer - a natural number, 0, or a negative natural number Integral - the collective sum of something Intersection - a place where two or more geometric elements are in the same location Interval - a patterned difference in states, which often represents as a number (e.g., 3 to 5 to 7 is an interval increase of 2). Inversion - reversing a shape Knot - a circle tangled in Euclidean space Line - an imaginary direction that extends forever both ways, represents a dimension Line segment - aka segment, a portion of a line, typically indicates some type of shape in more than one dimension Manifold - a topological space where each point represents something like Euclidean space (e.g., a science fiction wormhole) Matrix - a rectangular array of things Multiplication - aka times, adding a second value multiple times to a first value, is commutative Natural number - a clear-cut number that represents itself in nature as we perceive it (e.g., the numbers 2 or 15) Net - a two-dimensional cross-section of a three-dimensional object Non-commutative - where changing the order of things changes the results (e.g., 5-2 is *not* the same as 2-5) Non-Euclidean space - theoretical realms of space that don't abide by our 3-dimensional reality Nonlinear - where the outputs of something aren't proportional to the inputs Number - a clear, precise representation of quantity Numerator - the top part of a fraction that is denominated by the denominator Operation - a mathematical action guided by defined rules, uses an operator, can be commutative Operand - the object of an operation Operator - a formal language symbol that indicates what logical rules should be followed, works on an operand Oval - a 1-sided 2-dimensional shape that's not a circle p-adic numbers - rational prime numbers that show a continuous pattern of decimals that aren't 0 Parallel - a condition where two lines, segments or rays will never touch intersect, opposite of perpendicular Parallelogram - a 4-sided 2-dimensional shape that's not a square and has sides that are parallel to each other Percent - aka per cent, a x/100 comparison to another number Per mille - aka per mil or per mill, a x/1000 comparison to another number Perfect square - an integer where a square root of itself is also an integer Perimeter - the line segments that make the outside of a 2-dimensional shape or the edges of a 3-dimensional shape Perpendicular - a condition where two lines, segments or rays are at right angles to each other, opposite of parallel Place value - the specific left or right placement of a number and its relative significance to other numbers (e.g., 1,000 is 10 times more than 100) Polyhedron - a 3-dimensional shape with flat polygon faces, straight edges, and sharp vertices, plural is polyhedra Prime number - a real number that can't be divided by anything but itself and 1 Primitive - a base component of a concept Primorial - the sum of all prime numbers up to a given number Prism - a polyhedron with two polygon faces parallel to each other and the other faces as parallelograms Probability - the chance of a thing happening, represented as a percent Probabilistic - applying statistical probability to other domains Proof - a means to indicate with [absolute deductive certainty](understanding-certainty.md) that a mathematical concept is true Quadrilateral - a 4-sided 2-dimensional shape Quotient - the number coming from the result of division, where the divisor divides the dividend Radius - a line segment with ends on a circle's center and its circumference Ratio - a comparative and scalable relationship between two numbers (e.g., 1:2) Rational - a number that can be expressed as a fraction Ray - an imaginary direction that extends forever in one direction, contrast to a line Real - using integers to represent something, contrast to complex numbers Reality - an incidental and somewhat tenuous connection to math in general Rhombus - aka, equilateral quadrilateral, a 4-sided 2-dimensional shape where each side has the same length Rectangle - a 4-sided 2-dimensional shape that isn't a square and all the sides are at a right angle to each other Right angle - aka perpendicular angle, an angle at 90 degrees, happens to be *very* useful for many calculations Right triangle - a triangle with one of its corners at a 90 degree right angle Round - an approximated estimation relative to a number (e.g., 413 rounded to the nearest 100 is 400) Set theory - the logical study of sets, which are collections of things Shape - an object with a defined form, exists in at least one dimension on a plane Sphere - a 1-sided 3-dimensional shape where the distance is the same from the center Square - a 4-sided 2-dimensional shape where each side has the same length and all the sides are at a right angle to each other Square root - A result number that, if squared, would be the original number (e.g., √9 = 3), represented by the radical symbol, contrast to exponent Subtraction - aka taking away, demarcating and separating grouped values, is *not* commutative Surface area - the measured exterior surface of a 3-dimensional shape, similar to area for 2-dimensional objects Symmetry or Equivariance - a condition where a shape is the same on both sides, can be reflectional (mirrored), rotational (can be rotated to match), translational (can be moved without changing shape), helical (translational + rotational), scale (can change size while keeping shape), glide (reflectional + translational), and rotoreflection (reflectional + rotational) Synthetic or Axiomatic - Using subjective language instead of discrete reference points, contrast to analytic Topological - where geometry isn't easy to accurately measure with numbers Triangle - a 3-sided 2-dimensional shape Variable - a clearly specified number that's undefined for the purposes of the math problem (e.g., x represents any possible number, but we don't know yet) Vertex or Vertices - a point where two or more curves, lines, or edges meet, plural is vertices