—For a real number n, if n < 0 then its absolute value is –n, otherwise it is n. In other words, the absolute value of a number other than zero is always positive.

—The rate of change of velocity or speed.

—An angle smaller than a right angle.

—A transformation that preserves parallel lines.

—The force experienced by an object moving through the air, resisting the motion; also called fluid resistance or drag.

—The result of finding the values of the unknowns in an equation in general terms of the other variables in the equation; compare this with numeric solution.

—A computational process consisting of a number of predefined calculations that take on particular arguments (essentially a program with inputs).

—The process by which a line vector is converted to hard-edged pixels; compare this with antialiasing.

—The general illumination of a region as a result of light reflected in all directions (the amount of illumination in areas of shadow); see also directional light, attenuated light.

—The maximum distance from equilibrium achieved by an oscillator during any oscillation.

—A measure of rotation, defined as a fraction of a circle and usually measured in degrees or radians.

—The angle at which an object or wave strikes a surface.

—The angle at which an object or wave bounces off a surface after colliding with it.

—The number of rotations completed by a rotating object in a particular time period (see frequency).

—The angle turned through by a rotating object in a particular time period.

—The process by which a line vector is converted to smooth-colored pixels by gradually interpolating its color with the background.

—A variable provided as an input to a mathematical or programming function.

—A polygon or polyhedron used to create a simplified description of an object for the purposes of collision detection; compare this with collision map.

—Of some operator #, says that for each a, b, c in the domain, a # (b # c) = (a # b) # c (for example: a + (b + c) = (a + b) + c); compare this with commutative, distributive.

—A line or plane such that the graph of some function approaches it infinitely closely.

—Light emitted from a particular point, which diminishes with distance as a result of spreading out; see also ambient light, directional light.

—A generic word for various kinds of “middle” value of a set of values; most commonly the mean.

—Of a Cartesian space, a line through the origin, parallel to one vector of the basis.

—The line around which an object is rotating.

—A texture map in which lighting calculations have been made in advance.

—The study of objects in motion when acted on only by the force of gravity.

—A homogeneous coordinate system where the coordinates of a point P are given by the (signed) areas of the three triangles made between P and three predefined points A, B, C.

—A set of vectors, together with a defined origin, used to define a Cartesian space (or any other vector space).

—A spline defined by a cubic function between successive control points, with a defined tangent at each control point; compare this with Catmull-Rom spline.

—A system for working with “Boolean numbers”: numbers that can take only two possible values, TRUE and FALSE, using operators such as AND, OR, and NOT.

—For some shape in 3-D space, a volume of space entirely enclosing the shape; similarly “bounding area.”

—A partitioning tree in 3-D space (similarly, “bounding area hierarchy” in 2-D) in which objects are divided into successively smaller regions that enclose smaller sets.

—A method for finding the approximate numeric solution to an equation by narrowing down an interval within which the solution is to be found.

—A method for searching through a search tree by examining each possible branch at a particular level; compare this with depth-first search.

—A texture map describing the height of a surface at particular points.

—The study of infinitesimally small values, particularly integration and differentiation.

—The set of numbers that define the position of a point in Cartesian space under some basis.

—A two-dimensional Cartesian space.

—(also called Euclidean space): a set of points defined by a vector of n real numbers such that every triangle of points has three angles summing to 180° (very briefly!).

—A spline defined by a cubic function between successive control points, such that each curve segment is determined by four control points, creating a smooth transition; compare this with Bezier curve.

—For any object, the point such that for any line or plane through the point, half the object’s mass is on each side of the line.

—The force exerted by a rotating object moving in a circle; compare this with centripetal force.

—The force required to keep an object moving in a circle; compare this with centrifugal force.

—The center of mass of a triangle.

—In a tree, a node x is a child of node y if and only if y is the parent node of x.

—A shape defined as the locus of a point at a constant distance r from another point in a given plane.

—The perimeter of a circle.

—The constant part of a term in an expression: so the coefficient of the term 4x is 4.

—The constant of proportionality relating the extension of a stretched spring to the tension.

—The constant of proportionality μ relating the force perpendicular to the interface between two surfaces to the frictional force that resists their motion.

—Of three or more points, means that they lie in a straight line.

—An image map describing an object’s shape in simplified form for the purposes of collision detection; compare this with armature.

—For two values a and b, a number (or expression) that is a factor of both a and b.

—Of some operator #, says that for each a and b in the domain, a # b = b # a (for example: a + b = b + a); compare this with associative, distributive.

—The set of numbers that can be represented as the sum of a real number and an imaginary number, denoted by the symbol C.

—The length of a vector when projected in a particular direction. If the direction is defined by some unit vector u, then the component of the vector v in that direction is found by the scalar product v · u; sometimes as “the components of a vector” means its components in the directions of the underlying basis.

—A natural number that is not prime.

—A measure of the time taken for an algorithm to run, as a function of the size of its arguments.

—Of a shape, means that it is not convex.

—The surface of rotation of a line rotated about a non-parallel line in space; compare this with cylinder.

—Two integers a and b are congruent modulo a particular base m if and only if a = b + nm for some integer n.

—Of a complex number or quaternion, the result of taking the number and changing the sign of the imaginary part.

—The law stating that for any set of objects with no net force acting on them (other than those included in potential energy calculations), the total energy of the system is constant.

—The law stating that for a system of particles moving with no external force, the total momentum of the system is constant.

—An element in a function that is considered to be fixed when evaluating the function.

—See proportional.

—Of a spline, a point defining the shape of the curve in some way, usually a point on the curve.

—Of a shape, means that any line drawn between two points on the perimeter does not pass outside the shape; compare this with concave.

—See Cartesian coordinates.

—Two natural numbers a and b are said to be coprime if and only if their greatest common divisor is 1.

—A set whose elements can be listed in some order, even though the list may continue forever (they can be put in a one-to-one correspondence with the natural numbers).

—See natural numbers.

—Two or more oscillators that are connected, so that each exerts a force on the other.

—Of some value, the point at which the behavior of a system changes qualitatively, for example, the critical angle at which light cannot escape from a particular medium due to refraction.

—See vector product.

—A polynomial of degree 3.

—A set of connected points in space definable by a single continuously varying parameter.

—The surface of rotation of a line rotated about a parallel line in space; compare this with cone.

—The motion of an oscillator that would normally undergo simple harmonic motion but is also experiencing a damping factor.

—A factor opposing the motion of an oscillation, proportional to the speed.

—Of a polynomial function f(x), the largest exponent of x, so the function x³ + 2x has degree 3.

—A unit of angle, defined as 1/360 of a circle.

—In a fraction, the number on the bottom (also called the “divisor”).

—A method for searching through a search tree by examining a particular branch until it succeeds or fails, then backtracking; compare this with breadth-first search.

—The function g that gives the gradient of some other function f for each value of its arguments; compare this with integral, and see rate of change.

—The “magnitude” of a matrix: the amount by which the matrix scales a cube when used as a transformation.

—A line connecting two vertices of some shape; more specifically, the longest possible such line.

—The result of subtracting two values.

—An equation relating a function to its various derivatives.

—The process of finding the gradient of some function (the derivative).

—A phenomenon where a wave changes shape as a result of passing through a small gap, acting as if the gap were a new emitter for the wave.

—(also Lambertian reflection) Light emitted from a surface as a result of light incident on the surface, with no preferred direction; compare this with specular reflection.

—Of a vector or Cartesian space, the number of components or basis vectors required to define it.

—Light emitted in a particular direction, with no presumed diminution over distance (for example, sunlight); see also ambient light, attenuated light.

—A number derived from the parameters of a function whose value can be used to classify the behavior of the function in some way, for example, to find the number of its roots.

—The vector from one point to another.

—The length of a line from one point to another, defined as the magnitude of the vector between them.

—Of some operators # and @, says that for each a, b, c in the domain, a # (b @ c) = (a # b) @ (a # c), for example, a × (b + c) = (a × b) + (b × c); compare this with commutative, associative.

—See factor.

—The set of values for which a function is defined.

—A phenomenon where a wave has a different frequency in a different reference frame.

—See scalar product.

—See air resistance.

—The number 2.718... such that the function x → e^x has a derivative equal to itself.

—The amount by which an ellipse deviates from a circle, defined by where a and b are the halfmajor and halfminor axes, respectively.

—The proportion of energy used in some system which is converted to useful work.

—The maximum extension of a stretched spring for which the coefficient of elasticity remains valid.

—The potential energy of an object under the influence of a stretched spring or elastic.

—The locus of a point in a plane whose total distance from two defined points is constant.

—The result of an affine transformation applied to a sphere.

—The collective behavior of a group of simple interactive processes.

—A measurement of the amount something is moving, or could move given an opportunity; see also kinetic energy, potential energy, gravitational potential energy, elastic potential energy, and conservation of energy.

—A statement that two values are equal to one another, usually with one or more unknowns.

—A 2-D shape with three sides of equal length.

—A state of a system of objects where there is no net force.

—A function evaluating how likely a particular solution to a problem is to be near to the correct answer.

—See Cartesian space.

—The power to which a number has been raised, so in the term x⁵, x has an exponent of 5.

—Of a function, says that it behaves similarly to the power function mapping x → e^x; compare this with logarithm.

—A function consisting of a combination of terms, such as 3y² + 10xz –5(x³ – 2).

—The amount a spring or other elastic material is stretched from its natural length (see elastic limit).

—For two values a and b, a is a factor of b if and only if b is an integer multiple of a.

—The process of separating a function or number into a multiple of two or more factors.

—The area visible at a particular distance from a camera; alternatively the angle subtended by the viewport at the camera.

—A set with a limited number of elements.

—Of an ellipse, one of the two points which define it (pl. foci).

—An equation containing more than one variable, which relates these quantities to one another (usually defining one variable as a function of the others). Formulas do not have unknowns; they are assumed to be true for all possible (true) values of their variables.

—The result of dividing one number by another. (When both numbers are integers, this is a rational number.)

—The number of complete oscillations completed by an oscillator in a particular time; compare this with period.

—The force experienced between two surfaces parallel to their direction of motion, resisting the motion, proportional to the force between them perpendicular to their surfaces; see coefficient of friction.

—A 3-D shape formed by taking any kind of pyramid or cone and cutting off the top.

—The point or line around which a lever or other object rotates; its axis of rotation.

—A mapping from one set of values (the domain) to another (the range). A function can be represented algebraically (f: x → x³ or more succinctly f(x) = x³) or simply by a description (f(n) = 1 if n is odd, –1 otherwise).

—A function defining all possible solutions to a differential equation in terms of parameters remaining to be defined by the initial conditions; compare this with particular solution.

—A method for searching through a search space by “evolving” solutions using an analogue of natural selection.

—The highest value of some function for any value of its arguments (similarly “global minimum”); compare this with local maximum.

—The slope of a line in some Cartesian space, defined by the vertical distance moved divided by the horizontal distance for some infinitesimal movement.

—Either a picture of a function created by plotting its values against its arguments, the Cartesian plane on which this happens, or a set of nodes connected together by edges.

—The potential energy of an object under the influence of gravity.

—For two natural numbers a and b, the largest number which is a common factor of both.

—An algorithm that searches preferentially for a local solution to a problem.

—Of an ellipse, half of the distance between the two most extreme points on the perimeter (along the line through the two foci). The halfminor axis is then the longest distance from this line to the perimeter.

—A method of representing a point in a space of n dimensions by a projection of a line in n + 1 dimensions.

—In a right-angled triangle, the side opposite the right angle.

—A value which leaves all other values unchanged under some operator. For example, the identity function f(x) = x, the identity matrix which has 1s in the leading diagonal and 0s elsewhere, the number 0 under addition or 1 under multiplication.

—To say one statement is true “if and only if” the other is true means that either both are true or both are false (sometimes written “iff”).

—An image (usually in 2-D) that is projected to a surface by some mapping, or vice versa, to represent some property of the surface; see also collision map, texture map, bump map.

—Any multiple of the value i, defined as the square root of –1. The set of imaginary numbers is in a sense perpendicular to the set of real numbers.

—Two or more simultaneous equations, none of which can be derived from the others.

—A statement that two values are related to one another in some way (for example, that one is greater than the other); compare this with equation.

—See mass.

—Facts about the initial state of a system that allow you to deduce its later behavior, particularly when using a differential equation.

—For two values (numbers or expressions) a and b, b is an integer multiple of a if and only if there is some integer n such that b = an; compare this with factor.

—The set of natural numbers combined with the set of negative natural numbers (..., –2, –1, 0, 1, 2, ...) and denoted by the symbol Z.

—The function f that gives the (signed) area of an infinitesimally thin slice between some other function g and the axis (indefinite integral), or by substituting two values for its arguments, the area under the curve between those two points (definite integral). The inverse of the derivative.

—The process of finding the area between a graph of some function and the horizontal axis (the integral).

—For a function f(x), the value f(0).

—The process of finding an intermediate value between two other values by parameterizing the line between them.

—A set of real numbers, which may be “open” (not containing its end points, as in the set –1 < x < 0) or “closed” (containing the end points, as in the set -1 < x < 0), or a mixture of the two.

—The inverse of a one-to-one function f, denoted f^–1, is defined over the range of f such that if f(x) = y, then f^–1(y) = x. Equivalently, f^–1(f(x)) = x for all x in the domain of f. A many-to-one function can also be loosely defined to have an inverse by restricting the domain or accepting a multivalued function.

—The process of calculating the motion required by a series of connected rigid bodies to achieve a particular goal.

—Of a square matrix M, with non-zero determinant, the matrix M^–1 such that M^–1M = M M^–1 = I, where I is the appropriate-sized identity matrix.

—Two values x and y are inversely proportional if there is some constant k such that for all valid values of x and y; compare this with proportional.

—A formula relating two quantities x and y, saying that x is inversely proportional to the square of y.

—The set of real numbers, such as π and the square root of 2, which are not rational.

—A triangle with two of its sides having equal length.

—An algorithm that works by successively using the results of each step in the next; compare this with recursive function.

—The energy of a moving object, defined as half the square of its speed multiplied by its mass, with similar calculations for angular velocity.

—The friction between two surfaces moving relatively to each other; compare this with static friction.

—See diffuse reflection.

—An idealized object in three-dimensional space with a thickness of 0.

—Also called a “physical law,” a formula that states some kind of supposedly fundamental truth about the physical world, usually false.

—Of a matrix (m_ij), the values along the diagonal from top left to bottom right, with values m_ii.

—Of a tree, a node with no children.

—A curve of points with position vectors a + tv for some vectors a and v and some value 0 ≤ t ≤ 1.

—A polynomial of degree 1.

—A value of some function f for some values of its arguments such that all values of f for nearby arguments are less (similarly “local minimum”); compare this with global maximum.

—The set of points with a particular property (for example, a straight line is the locus of a point in a plane at an equal distance from two other points).

—The inverse of the power function: for two numbers a and b, a number x such that b^x = a. b is called the “base.”

—For two natural numbers a and b, the smallest number that is an integer multiple of both a and b.

—Of a fraction, means that the numerator and denominator are coprime.

—The length of a vector defined by the Pythagorean formula as the square root of the sum of its components.

—Of a function, states that several elements in the domain can map to the same element in the range; compare this with one-to-one function and multivalued function.

—See function.

—The property of matter that defines how much force is required to make it accelerate; also called “inertia.”

—A two-dimensional array of real numbers.

—A point on the graph of some function where it is at its highest. For a smooth curve, the gradient is zero; see also local maximum, global maximum.

—For n values, the sum of the values divided by n; compare this with average.

—The study of objects in motion or equilibrium.

—A shape in a computer-generated 3-D world, consisting of a number of vertices connected by polygons.

—In a game, the move for any player that minimizes their maximum possible loss (equivalently, maximizes their minimum possible gain), hence an algorithm making use of this concept to find the best strategy for playing a game.

—A point on the graph of some function where it is at its lowest. For a smooth curve, the gradient is zero; see also local maximum, global maximum.

—A texture map in several variants of different sizes used to create smooth shading over distance.

—A shape created in a computer-generated 3-D world, made from a mesh.

—A function mapping the set of integers to the finite set {0, 1, ..., m –1) for some natural number m, by mapping each number to its remainder when divided by m; also called a “congruence relation.”

—The angular equivalent of mass, which for a particle is equal to the product of its mass and the square of its distance from the axis of rotation.

—The product of an object’s mass and velocity; see conservation of momentum.

—Of a function, states that some elements in the domain can be mapped to more than one element in the range (though this is not a function in a strict definition of the word); compare this with one-to-one function and many-to-one function.

—The set of “counting numbers” including zero (0, 1, 2, ...) denoted by the symbol N.

—A graph in which the edges have been assigned a value, usually representing a “cost” of some kind.

—A virtual object, such as a vertex of a graph or element of 3-D space.

—Of two vectors, means that they are perpendicular. Of a surface, means a vector perpendicular to the surface.

—Of a vector, the result of dividing it by its magnitude to get a unit vector.

—In a fraction, the number on the top (also called the “dividend”).

—The result of finding the values of the unknowns in an equation by searching for the specific numbers which make the equation true (as opposed to an algebraic solution).

—An angle greater than a right angle but less than a straight line.

—See quadtree.

—Of a function, states that each element in the domain is mapped to exactly one element in the range, and vice versa; compare this with many-to-one function and multivalued function.

—A function that maps one or more arguments from a particular set to a single result in the same set. You usually think of the binary operators such as +, –, ×, ÷

—A point defined as the starting point of some basis.

—Of two or more vectors, means that they are mutually at right angles.

—A basis where the basis vectors are orthogonal and have a magnitude of 1.

—A motion that repeats over time, such as a bouncing spring or an object bobbing on water; see frequency, period, amplitude.

—Of two oscillations, means that they have the same frequency but their phase is different, or specifically is half the period.

—Of two vectors, the operator that creates a vector from the products of each component of the arguments, for example, the pairwise product of the vectors (2 3) and (1 –2) is the vector (2 –6).

—A curve in two dimensions; the graph of a quadratic function.

—Of two vectors, means that one is a scalar multiple of the other. Of two lines, means that any vector on one is parallel to any vector on the other.

—A quadrilateral with two pairs of parallel sides.

—An element in a function that can be varied to create a family of different functions with similar properties.

—Defining some curve or surface in terms of a parametric equation.

—A set of formulas relating one or more variables to one or more real-valued parameters.

—In a tree, the node next in line from any particular node toward the root node; compare this with child node.

—The derivative of a curve drawn on a surface.

—An idealized object in space, with a size of zero but some mass, as well as perhaps other properties.

—A function for which a differential equation holds true, given particular initial conditions; compare this with general solution.

—A tree representing a group of objects in space according to their relative positions.

—The curve or surface defining the outer border of some shape.

—The time taken for some oscillator to complete a single oscillation; compare this with frequency.

—Of two vectors, means that they are at right angles; compare this with orthogonal.

—Altering a value by some small amount.

—Of two waves with the same waveform, the distance by which their wavefronts are separated at a particular time.

—The locus of a point in space at the same distance from two defined points. Equivalently, it has position vector a + tv + sw, where a, v, and w are defined vectors and t and s are parameters.

—In a game, a move by one player.

—A point on the graph of some function where its second derivative is zero.

—A closed shape made up of a number of straight line segments connecting the same number of vertices.

—A closed 3-D shape whose perimeter is a number of polygons joined by straight edges.

—A function in one variable, consisting entirely of terms of the form axⁿ, such as 2x³ + 3x²–4.

—A vector from the origin to a particular point.

—The energy held by an object under the influence of an external force, particularly gravity, a stretched spring, magnetic fields, etc. Generally, the amount of work a system is capable of doing.

—A number obtained by multiplying a value by itself a certain number of times, so 8 is the third power of 2, denoted 2³. More generally, it can be defined as the power function mapping pairs of numbers to either a real or a complex number.

—The amount of work done (energy released or used) by a system or machine over time.

—For two natural numbers a and b, a prime number that is a factor of both a and b.

—A natural number greater than 1 with no factors other than itself or 1.

—The principle that all physical calculations should be independent of the reference frame within which they are calculated.

—The result of multiplying two values.

—An object moving under gravity.

—A map that reduces the number of dimensions of a space, such as mapping a sphere to a circle.

—The virtual plane in space representing the position of the image you are looking at through a particular camera.

—Two values x and y are proportional, or “in proportion,” if there is some constant of proportionality k such that x = ky for all valid values of x and y; compare this with inversely proportional.

—An area of the Cartesian plane such that all the points are of the same sign in each of their coordinates.

—A polynomial of degree 2.

—A four-sided polygon.

—A partitioning tree in 2-D space, in which objects are divided according to their position within successively smaller squares (in 3-D, an octree).

—A special kind of 4-D vector, the vector equivalent of a complex number.

—Either the result of dividing one number by another (see fraction) or the integer part of this division (see modulo).

—A unit of angle, defined as of a circle.

—The distance of a point on the circumference of a circle from its center.

—In column number notation, the dot that signifies the end of the integer part of the number.

—The set of values returned by a function.

—The amount by which a value changes over time, equivalent to the derivative with respect to time.

—The set of numbers that can be represented as a fraction of two integers, denoted by the symbol Q.

—A line in 3-D space from a given point to infinity.

—The set of numbers that can be represented on an infinitely precise number line, denoted by the symbol R.

—For any number n, the fraction .

—Of a system of lines, means that any two are either parallel or perpendicular.

—An algorithm that works by calculating each step in terms of the same algorithm applied to a simpler case, until it finds a case simple enough to solve directly; compare this with iterative function.

—A process of deduction where you prove something to be true by assuming it is false and deducing a contradiction: “if x were true then y would be true, but you know y is false therefore x must be false.”

—In a physical situation, the basis of the physical space along with a reference velocity used to define all other calculations; see principle of relativity.

—A transformation that moves each point to another point opposite it in some mirror line or plane.

—An angle greater than two right angles.

—A phenomenon where a wave changes its direction of travel as a result of changing its speed.

—When dividing one natural number n by another, m, the value r such that 0 < r < m and n = am + r for some natural number a.

—A phenomenon where an oscillation gradually increases in amplitude, as a result of an oscillating force of the same frequency.

—A parallelogram whose sides are all of equal length.

—An angle of 90 degrees or radians.

—A triangle with one of its angles being a right angle.

—A transformation which preserves angles between lines.

—Of a function f, a value x such that f(x) = 0.

—Of a tree, the node with no parent.

—A transformation that moves each point by some angle around a particular center.

—Of a surface, a point which is a local maximum in one direction and a local minimum in another.

—A value that is not a vector, that is, it has no direction; alternatively, a vector of dimension 1.

—The sum of the pairwise products of the components of two vectors, written with a dot as u · v: for example, the scalar product of the vectors (2 3) and (1 –2) is the sum 2 × 1 + 3 × (–2). (Also called the “dot product.”)

—A transformation that moves each point to some multiple of its vector relative to some reference point.

—The set of all potential solutions to a problem.

—A tree representing all the possible moves in a game, or equivalent for similar problems, which some algorithm is sought to solve.

—A collection of objects (“elements”), which may be finite (the set {1, 3, 5, 7}), countable (the set of all odd numbers), or uncountable (the set of all numbers between 0 and 1).

—A transformation that moves each point by a multiple of a vector, parallel to some reference line or plane, proportionally to its distance from this line or plane.

—Of a value, indicates that it may be positive or negative (for example, the signed distance of a point from a line is positive in one direction, negative in the other).

—Of two shapes, says that they are identical except for a scale transformation.

—A sinusoidal oscillation, generally associated with the motion of a stretched spring; compare this with damped harmonic motion.

—The process of manipulating a function or statement algebraically to put it into a more tractable form.

—Two or more equations in the same unknowns, which are all considered to hold true for the same set of solutions.

—Having the form of the function A sin(ωx + c), where A is the amplitude, ω is the frequency, and c is the phase.

—Light reflected from a surface directly, such that the angle of incidence equals the angle of reflection (mirror reflection); compare this with diffuse reflection.

—The distance traveled by a moving object over time.

—The locus of a point in (usually 3-D) space at a constant distance from a particular center.

—A curve defined by some parametric function.

—An object that can extend, experiencing a tension as a result, and may also be compressed; see extension, coefficient of elasticity.

—Either a planar shape with four sides of equal length and four right angles, or the result of multiplying a number by itself.

—A matrix that has the same number of rows as columns.

—The inverse of the square function x²: the square root of x is a number that when multiplied by itself gives the answer x.

—In a game, a set of strategies for the players such that if any single player changes strategy, they do worse than before.

—A measure of the spread of a set of values, defined as the square root of the mean squared distance of the values from their own mean.

—A numerical “sentence” relating some values to one another.

—The friction between two surfaces exerting a force on one another but not moving relatively to each other; compare this with kinetic friction.

—The process of evaluating a function for a particular set of values of its arguments.

—If you draw a triangle from some point P to two points on the perimeter of an object, the angle at P for the largest possible such triangle is said to be the angle subtended by the object at P. (P is often an observer of the object.)

—The result of adding two values.

—A set of connected points in space definable by a pair of continuous parameters.

—For some function f(x), the locus of a point in 3-D space whose perpendicular distance from the x-axis is equal to f(x) at any x-coordinate.

—A straight line (or plane) that touches some curve or surface at a particular point without passing through it. (In other words, it has the same gradient as the curve at that point.)

—Of a sequence of values a₁, a₂, ..., this says that there is some value x such that for any small number d, you can find a number N such that for every n > N, |a_n–x| < d.

—The force in an object being pulled from each end, such as a string or spring.

—A generalization of the concepts of vector, matrix, and scalar; an array of values in one or more dimensions.

—An element of an expression consisting only of a constant value multiplied by some combination of variables, such as 5xy².

—The maximum downward speed of a falling object as a result of the air resistance, or generally of any object experiencing drag or friction.

—A point of a texture map.

—An image map describing the reaction of a surface to light at particular points.

—The study of the shapes of objects without reference to distance, using only notions of connectedness, holes, twists, etc., hence, these properties of an object.

—The angular equivalent of force, defined as force × perpendicular distance from the axis of rotation.

—A 3-D shape, the locus of a point whose perpendicular distance from a particular circle is constant.

—A special kind of 4 × 4 matrix representing an affine transformation of homogeneous coordinates.

—A map from one set of points to another in some space.

—A transformation that adds a constant vector to each point in the space.

—Of a matrix M, describes the matrix whose rows are the columns of M and vice versa.

—A quadrilateral with a pair of parallel sides.

—A graph in which each node has exactly one parent (except the root node) and zero or more children, and with no loops.

—The functions relating the angles in a right-angled triangle to the lengths of its sides.

—Formulas relating the various trigonometric functions to one another.

—The study of the properties of triangles.

—A point on the graph of some function where its derivative (and all partial derivatives for a surface) is zero. May be a maximum, minimum, point of inflection, or saddle point.

—A set with an infinite number of elements that cannot be listed even in infinite time.

—A vector with a magnitude of 1.

—An element in an equation or other statement whose value is to be found by presuming the statement to be true.

—A method for evaluating a particular solution to a search problem when using for example, a genetic algorithm.

—An element in a function that can be replaced throughout by some value from the domain in order to return some other value (also called an “argument”); also a generic term used to cover constants, parameters, and unknowns.

—An ordered set of two or more real numbers (or other values more generally) that can be added together by adding their components, and can be multiplied by a scalar.

—The 3-D vector formed by combining two other such vectors such that its magnitude is equal to the product of their magnitudes with the sine of the angle between them, and its direction is perpendicular to both. (Also called the “cross product.”)

—The vector traveled by a moving object over time; the vector equivalent of speed.

—A corner of a shape. In a graph, equivalent to a node (pl. vertices).

—The volume of space visible from a particular camera.

—The area of the projection plane visible on the screen.

—Light whose wavelength lies within the range detectable by the human eye (approximately 10^–7).

—A phenomenon where a group of coupled oscillators transfer energy from one place to another.

—The shape of the graph of a particular wave measuring distance from equilibrium through space.

—The surface in space representing equivalent points in the oscillation of a wave as it travels.

—The distance between successive wavefronts of a wave.

—The force acting on an object as a result of gravity, proportional to its mass.

—Of a set of values x₁, x₂,..., the result of adding together the values multiplied by some predefined values w₁, w₂,..., in other words, the sum .

—The energy given up by an object to induce movement in some other object.

—A game in which players compete for “money,” where at each stage, the total amount of “money” is constant.