Math Terms

What is a Trapezoid – Definition, Properties & Formula

This article explains what a trapezoid is — a quadrilateral with exactly one pair of parallel sides — and covers its key properties, angle relationships, midsegment theorem, and area formula with worked examples. You will be able to identify a trapezoid, distinguish it from a parallelogram, and solve any standard exam problem involving its measurements.

What is Diameter – Definition, Formula & Examples

This article explains what diameter is — the longest chord of a circle, equal to twice the radius — and shows how the diameter formula connects to circumference and area, with worked examples throughout. You will leave with a clear, exam-ready understanding of diameter and how it relates to every other circle measurement.

What is a Line in Math? Definition, Types, Examples

A line in math is a straight, one-dimensional figure that extends infinitely in both directions. It has no width or thickness — only length. A line is one of the most fundamental objects in geometry, alongside the point and the plane

What is Difference in Math? Definition, Examples

In math, the difference is the result of subtraction** — the answer you get when you subtract one number from another. In $10 - 4 = 6$, the 6 is the difference. The number you start with is called the minuend (10), the number being subtracted is the subtrahend (4), and the result is the difference.

What is a Scalene Triangle? Definition, Properties

A scalene triangle is a triangle with no equal sides and no equal angles — every side is a different length, every angle is a different measure. The three angles still sum to 180°. Area is computed by $A = \tfrac{1}{2}bh$ or by Heron's formula $A = \sqrt{s(s-a)(s-b)(s-c)}$.

What is a Sphere? Definition, Volume, Surface Area

A sphere is a perfectly round 3D shape — the set of all points in space at the same distance from a fixed centre. That distance is the radius $r$. The volume of a sphere is $V = \tfrac{4}{3}\pi r^3$ and the surface area is $SA = 4\pi r^2$. A sphere has the *smallest surface area* enclosing a given volume — which is why bubbles are spherical.

What is a Variable in Math? Definition, Types

A variable in math is a letter that stands for an unknown or changing value — typically $x$, $y$, $z$, $a$, $b$, or $n$. Variables are the language of algebra. There are two main types: independent variables (the input you choose) and dependent variables (the output that depends on the input).

What is a Reciprocal? Definition, Formula, Examples

The reciprocal of a number is 1 divided by that number. For any non-zero number $x$, its reciprocal is $\frac{1}{x}$, written as $x^{-1}$. When a number is multiplied by its reciprocal, the result is always 1 — that's why the reciprocal is also called the multiplicative inverse. To find the reciprocal of a fraction, flip it: the reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$. The number $0$ has no reciprocal.

What is Vertical? Definition, Equation, Examples

Vertical in math means straight up-and-down, perpendicular to the horizon. A vertical line on the coordinate plane is parallel to the y-axis. Every point on the line has the same x-coordinate. The equation is $x = a$ where $a$ is a constant. Vertical lines have undefined slope (not zero — undefined).

What is an Isosceles Triangle? Definition, Properties

An isosceles triangle is a triangle with two sides of equal length — called the legs — and two equal angles opposite those sides — called the base angles. The third side is the base, and the angle between the two legs is the vertex angle. Six properties follow from this single definition.

What is the Radius of a Circle? Definition, Formula

The **radius** of a circle is the distance from the centre to any point on the circumference. It is exactly **half the diameter**: $r = d/2$. The radius is the most fundamental measurement of a circle — area ($A = \pi r^2$), circumference ($C = 2\pi r$), and every other circle formula depends on it.

What is Horizontal? Definition, Meaning, Examples

Horizontal in math means parallel to the horizon — running left-to-right (or right-to-left) without rising or falling. A horizontal line is parallel to the x-axis, has the equation $y = b$ where $b$ is constant, and has slope 0.

What is Calculus? Definition, Branches, Examples

Calculus is the branch of mathematics that studies continuous change — how quantities change over time, or how shapes accumulate area or volume. It has two main branches: differential calculus and integral calculus. The two are connected by the Fundamental Theorem of Calculus.

What is an Algorithm? Definition, Examples

An algorithm is a finite, well-defined sequence of instructions that solves a specific problem or performs a computation. The word comes from al-Khwarizmi, a 9th-century Persian mathematician whose name was Latinised as Algoritmi.

What is Area? Definition, Formula, Examples

Area is the size of a two-dimensional surface — how much space a flat shape occupies. It is measured in *square units* (m², cm², ft², in²). The most-used area formulas are: square ($A = a^2$), rectangle ($A = l \times w$), triangle ($A = \tfrac{1}{2} \times b \times h$), and circle ($A = \pi r^2$).

What is a Percent? Definition, Formula, Examples

percent (symbol: %) is a way to express a number as a fraction of 100. Percent means "per hundred" — so 25% means 25 out of 100, or $\tfrac{25}{100} = 0.25$. The formula to convert a fraction to a percentage is $\frac{\text{part}}{\text{whole}} \times 100$.

What is a Solution in Math – Definition & Examples

This article explains what a solution in math means — a value or set of values that satisfies an equation or inequality — and walks through examples across one-variable equations, systems, and inequalities. You will understand the formal definition, how to verify a solution, and why some equations have no solution or infinitely many.

What is Square Root – Definition, Formula & Examples

This article explains what square root means — the value that, multiplied by itself, gives the original number — and covers the square root formula, notation, and worked examples from perfect squares to estimating irrationals. You will understand the concept, the symbol, and the methods for finding square roots by hand and by calculator.

What is Perimeter – Definition, Formula & Examples

This article explains what perimeter is — the total length of a shape's boundary — and provides the perimeter formula for every standard polygon and circle, with worked examples that progress from straightforward to multi-step problems. You will leave with the definitions, formulas, and practice you need to solve any perimeter question with confidence.

What is a Real Number – Definition, Types & Examples

What is Frequency – Definition, Formula & Examples

What is Pi (π)? Definition, Value & Formula

Pi (π) is the ratio of any circle's circumference to its diameter, approximately 3.14159 or 22/7. It's an irrational, transcendental constant — its decimal expansion never ends and never repeats.

Symmetry in Math: Types, Lines of Symmetry & Examples

Symmetry in math is the property of a shape or object that looks unchanged after a transformation - reflection, rotation, or translation. The five main types are reflection, rotational, translational, point, and glide reflection symmetry, each defined by how the shape stays the same when moved.

Integer – Definition, Types, Examples & Properties

An integer is a whole number - positive, negative, or zero - with no fractional or decimal part, written as the set ℤ = {..., −3, −2, −1, 0, 1, 2, 3, ...}. Integers follow closure, commutative, associative, distributive, identity, and additive inverse properties, and form the foundation for arithmetic, the number line, and all rational numbers.

What is Probability? Definition, Formula & Examples

Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain), calculated using the formula P(E) = n(E) / n(S) - favourable outcomes divided by total outcomes. The three main types are theoretical (reasoned), experimental (observed from trials), and axiomatic (rule-based), and the concept underpins everything from coin tosses to weather forecasting and machine learning.

Volume in Math: Definition, Formula & Examples

Volume is the amount of 3D space an object occupies, measured in cubic units (cm³, m³). For most regular shapes it equals base area × height - cube (a³), cuboid (l × b × h), cylinder (πr²h) - while spheres use (4/3)πr³, cones are one-third of a cylinder, and irregular shapes are measured by water displacement.

Whole Numbers: Definition, Symbol, Properties & Examples

A whole number is a non-negative integer with no fractional or decimal part. The set of whole numbers is W = {0, 1, 2, 3, 4, 5, ...}, beginning at 0 and continuing infinitely. Numbers like 7, 42, and 1000 are whole numbers. Numbers like −3, 1/2, and 0.7 are not.

Parallelogram: Definition, Properties & Formulas

A parallelogram is a quadrilateral (a four-sided polygon) in which both pairs of opposite sides are parallel and equal in length. The word comes from the Greek parallēló-grammon, meaning "shape of parallel lines.

Vertex in Maths: Definition, Examples, and Types Explained

Odd Numbers: Definition, List (1–100), Properties & Examples

An odd number is any whole number that leaves a remainder of 1 when divided by 2 — ending in 1, 3, 5, 7, or 9 (like 1, 3, 5, 7, 9, 11... 99). They follow the form 2n + 1, can be consecutive (3, 5, 7) or composite (9, 15, 21), and obey simple rules: odd + odd = even, odd × odd = odd.

What is an Even Number? Definition, List & Examples

An even number is any integer that can be divided by 2 with no remainder. Examples include 2, 4, 6, 8, 0, and −12. Every even number can be written in the form n = 2k, where k is an integer.

What is a Rational Number? Examples and Types

Rational numbers are numbers expressible as p/q (integers, q ≠ 0) and cover integers, fractions, terminating decimals, and repeating decimals - denoted by Q. They split into positive, negative, zero, and standard form; stay closed under addition, subtraction, multiplication, and non-zero division; and differ from irrationals (π, √2) whose decimals never terminate or repeat.

What is a Composite Number? Definition, List & Examples

A composite number in maths is a whole number greater than 1 with 3 or more factors (like 4, 6, 9, 12). The smallest composite number is 4, and there are 74 composite numbers between 1 and 100.

What is a Natural Number? Definition, Examples & Properties

A natural number is any number used for counting, starting from 1 and going on forever - written as the set N = {1, 2, 3, 4, 5, ...}. They don't include negatives, decimals, or fractions, and whether 0 counts depends on the convention your textbook follows.

Median in Maths: Definition, Formula & Examples

The median is the middle value of an ordered data set. For ungrouped data with odd n, it's the ((n+1)/2)ᵗʰ term; for even n, it's the average of the two middle terms; for grouped data, use Median = l + [((n/2) − cf) / f] × h.

Rhombus – Definition, Properties, Formulas & Examples

A rhombus is a four-sided shape with all four sides equal in length, opposite sides parallel, and diagonals that bisect each other at right angles. Its area is (d₁ × d₂) / 2 and its perimeter is 4a, where d₁ and d₂ are the diagonals and a is the side length.

What is Mode in Maths? Definition, Formula, and Examples

Mode is the value that appears most often in a dataset - 7 is the mode of 4, 7, 7, 9, 12. Unlike mean and median, mode also works on non-numerical data like colors, blood types, or favorite subjects.

What is an Irrational Number? Definition, Examples & Properties

An irrational number is a real number that cannot be written as a ratio of two integers (p/q form), and its decimal expansion never terminates and never repeats. Common examples include √2, π, e, and the golden ratio φ.