Explore mathematical terms, formulas, history, and concepts — from Algebra to Zero
The absolute value of a number is its distance from zero on the number line, always non-negative.
Algebra is the branch of mathematics dealing with symbols and the rules for manipulating them to represent quantities and relationships.
An angle is formed by two rays sharing a common endpoint called the vertex.
Area is the measure of the amount of space inside a two-dimensional shape.
Arithmetic is the most elementary branch of mathematics dealing with numbers and basic operations: addition, subtraction, multiplication, and division.
An asymptote is a line that a curve approaches arbitrarily closely as it extends to infinity.
The average (mean) is the sum of all values divided by the number of values.
Base is the number of unique digits used in a numeral system, or the number being raised to a power in exponentiation.
A binomial is an algebraic expression with exactly two terms, such as a + b.
Calculus is the mathematical study of continuous change, comprising differential and integral calculus.
A chord is a line segment connecting two points on a circle.
A circle is the set of all points in a plane equidistant from a fixed point called the center.
A coefficient is a numerical or constant factor multiplied by a variable in an algebraic term.
A combination is a selection of items from a larger set where order does not matter.
A complex number is a number of the form a + bi, where a and b are real numbers and i = √(-1).
A constant is a fixed value that does not change, as opposed to a variable.
A coordinate system uses numbers (coordinates) to uniquely determine the position of a point in space.
Cosine is a trigonometric function defined as the ratio of the adjacent side to the hypotenuse in a right triangle.
A decimal is a number expressed in the base-10 numeral system, using a decimal point to separate whole and fractional parts.
The derivative measures the instantaneous rate of change of a function with respect to its variable.
The determinant is a scalar value computed from a square matrix that encodes important properties of the matrix.
The diameter is the longest chord of a circle, passing through the center and connecting two points on the circumference.
Differentiation is the process of finding the derivative of a function, measuring how it changes.
An ellipse is a curved shape formed by all points where the sum of distances to two fixed points (foci) is constant.
An equation is a mathematical statement asserting the equality of two expressions, connected by the equals sign (=).
An exponent indicates how many times a number (the base) is multiplied by itself.
The factorial of a non-negative integer n, denoted n!, is the product of all positive integers less than or equal to n.
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1.
A fraction represents a part of a whole, written as a numerator over a denominator (a/b).
A function is a relation between a set of inputs and a set of possible outputs, where each input maps to exactly one output.
Geometry is the branch of mathematics concerned with the properties, measurement, and relationships of points, lines, angles, surfaces, and solids.
The golden ratio (φ ≈ 1.618) is a mathematical constant where the ratio of the whole to the larger part equals the ratio of the larger part to the smaller part.
A graph is a visual representation of data or a mathematical function, showing relationships between variables.
The hypotenuse is the longest side of a right triangle, opposite the right angle.
An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.
The integral is a mathematical operation that finds the area under a curve, representing accumulation of a quantity.
Integers are whole numbers that can be positive, negative, or zero, but have no fractional or decimal part.
An inverse operation or function reverses the effect of another operation or function.
A limit describes the value that a function approaches as the input approaches a particular value.
A linear equation is an equation whose graph forms a straight line, typically in the form ax + b = 0 or y = mx + b.
A logarithm is the inverse operation of exponentiation, answering "to what power must a base be raised to produce a given number?"
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
The mean (arithmetic mean) is the sum of all values divided by the count of values.
The median is the middle value in a sorted dataset, dividing it into two equal halves.
The mode is the value that appears most frequently in a dataset.
Natural numbers are the counting numbers: 1, 2, 3, 4, ... (sometimes including 0).
A number is a mathematical object used for counting, measuring, and labeling.
A permutation is an arrangement of items in a specific order.
Perpendicular lines or planes intersect at a right angle (90°).
Pi (π) is the mathematical constant representing the ratio of a circle's circumference to its diameter, approximately 3.14159.
A polygon is a closed 2D shape made of straight line segments connected end to end.
A polynomial is an algebraic expression with one or more terms, each consisting of a coefficient multiplied by a variable raised to a non-negative integer power.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.
A proportion is an equation stating that two ratios are equal: a/b = c/d.
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a ≠ 0.
A quadrilateral is a polygon with four sides, four vertices, and four angles summing to 360°.
The radius is the distance from the center of a circle (or sphere) to any point on its circumference (or surface).
A ratio is a comparison of two quantities expressed as a quotient, showing how many times one contains the other.
Real numbers include all rational and irrational numbers, representing any value along the continuous number line.
The square root of a number is a value that when multiplied by itself gives the original number.
A sequence is an ordered list of numbers following a specific pattern or rule.
A series is the sum of the terms of a sequence.
A set is a well-defined collection of distinct objects, considered as a single mathematical object.
Sine is a trigonometric function defined as the ratio of the opposite side to the hypotenuse in a right triangle.
Slope measures the steepness and direction of a line, calculated as the ratio of vertical change to horizontal change.
A sphere is the set of all points in three-dimensional space at a fixed distance (radius) from a center point.
Statistics is the science of collecting, analyzing, interpreting, presenting, and organizing data.
A subset is a set whose elements are all contained within another set.
Tangent is a trigonometric function defined as the ratio of the opposite side to the adjacent side in a right triangle.
A transformation is an operation that moves, flips, or changes a shape to produce a new shape.
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.
Trigonometry is the branch of mathematics dealing with the relationships between angles and sides of triangles.
A variable is a symbol that represents an unknown or changeable quantity, typically denoted by letters like x, y, or n.
A vector is a quantity with both magnitude and direction, represented geometrically as an arrow.
A Venn diagram uses overlapping circles or shapes to show logical relationships between sets.
Volume is the measure of the amount of three-dimensional space occupied by a solid object.