# Glossary

A glossary of mathematical terms designed to provide clear and concise definitions. Each term in the dictionary is presented as an individual page, featuring a definition, similar terms, related terms, and visual representations.

A 30-60-90 triangle is a special type of right triangle where the three angles measure 30 degrees, 60 degrees, and 90 degrees.

A 45-45-90 triangle is a special type of right triangle where the three angles measure 45 degrees, 45 degrees, and 90 degrees. The three angles describe a unique geometry where the hypotenuse is a factor √2 larger than the adjacent and opposite sides.

An acute angle is an angle that measures less than 90 degrees.

An angle is a measure of rotation or turning and is usually measured in degrees or radians. In geometry, an angle is the figure formed by two rays, sharing a common endpoint called the vertex.

Area is a mathematical term that describes the amount of space inside a two-dimensional shape, like a square, rectangle, or circle. It's like counting the number of square units that can fit inside a shape.

An array is a computer programming construct for storing contiguous data. The data can be accessed by indexing into the array with the location of each element.

The average, also known as the mean, is a measure of central tendency. It is calculated by adding all the numbers in a list and dividing by the count of numbers in the list.

An axiom, in mathematics and logic, is a statement or proposition that is regarded as being self-evidently true, without the need for proof. Axioms serve as the starting points for developing a mathematical theory. Different sets of axioms can give rise to different, but consistent, mathematical systems.

A circle is a basic shape used throughout mathematics. A circle is defined as a shape where every point along its perimeter is an equal distance from its center.

A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

Complementary angles are a pair of angles whose measures add up to 90 degrees. When two angles are complementary, each angle is said to be the complement of the other.

A constant is a value that does not change or vary in a mathematical expression or equation. It is the opposite of a variable, which can take on different values. Constants can be numbers, symbols, or even functions that remain unchanged throughout a given problem or context.

A decimal is a number expressed in the base-10 numeral system, which uses the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Decimals can be used to represent whole numbers, fractions, or a combination of both.

Degrees are a unit of measurement for angles, representing the rotation between two rays. The degree angle system divides a full rotation into 360 units called degrees.

The determinant is a special number that can be calculated from a square matrix. It provides important information about the matrix and the linear map it represents, such as whether the matrix is invertible or the system of equations it represents has a unique solution.

The domain of a function is the set of all possible input values for which the function is defined.

A function is a mathematical relationship between two sets, called the domain and the codomain, in which each element in the domain corresponds to exactly one element in the codomain. Functions are often represented by equations, graphs, or tables and can model real-world scenarios or abstract concepts.

The golden ratio, often denoted as φ (phi), is an irrational number that has unique mathematical properties and appears in art, nature and, architecture. It is approximately equal to 1.61803398875.

The golden rectangle is a rectangle whose width divided by height is equal to the golden ratio (approximately 1.618). It is believed to have aesthetically pleasing properties and has been used in art, architecture, and design throughout history.

A graph is a visual representation of a function or a set of data in the Cartesian coordinate system. It helps in understanding the behavior of the function or the trend in the data. The horizontal axis is usually denoted as x-axis and the vertical axis as y-axis.

In mathematics, an identity is an equality that holds true for all values of the variables within its domain. It is a relationship between two mathematical expressions that are equal for all possible values of the common variables.

An implicitly defined curve is a curve that is described by an equation involving two or more variables, rather than by an explicit function in terms of one variable. The equation defines the relationship between the variables but does not explicitly provide one variable as a function of the other.

An integer is a number that can be written without a fractional or decimal component. It includes the natural numbers (1, 2, 3, ...), zero (0), and the negatives of the natural numbers (-1, -2, -3, ...). The set of all integers is often denoted by the letter Z.

An interval is a set of real numbers that lies between two given numbers. The two numbers that define the interval are often called the endpoints. Intervals can be open (not including the endpoints), closed (including the endpoints), or a mix of both.

In mathematics, a law refers to a universally accepted principle or rule that describes a particular mathematical relationship or property. These mathematical laws are typically proven truths, derived from axioms or basic assumptions, that hold under specific conditions.

In math, a matrix is a function that maps between two vector spaces. A matrix can also be thought of as a shorthand way to write a system of linear equations.

The mean of a data set is the average of all the values in the data set. It is calculated by adding all the numbers in a list and dividing by the count of numbers in the list.

The median of a data set is the middle value of the sorted data.

The mode of a data set is the most commonly occurring value in the data set.

A number is a mathematical object used to count, measure, and label. The main types of numbers include natural numbers, whole numbers, integers, rational numbers, real numbers, and complex numbers. Each of these types includes different sets of numbers and has different properties.

An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. It is larger than a right angle and smaller than a straight angle.

In mathematics, orthogonal refers to a concept involving right angles. In Euclidean space, two vectors are orthogonal if they are at right angles to each other. In linear algebra, two vectors are orthogonal if their dot product is zero. The term is also used in various other mathematical contexts with similar connotations.

In mathematics, a parameter is a quantity that influences the output but remains constant within specific scenarios. In statistics, parameters are values that represent characteristics of an entire population. In computer science, parameters are values passed to a function or method.

In geometry, two lines or planes are said to be perpendicular if they intersect at a right angle (90 degrees).

A perpendicular angle is equal to a quarter of a full rotation. A perpendicular angle is measured as 90 degrees or 1/4 τ radians.

In math, a plot is a visual representation of data points or a function on a coordinate system.

A point in geometry is a specific location in space, represented by coordinates in a given coordinate system. It has no dimensions, only position. In a two-dimensional space, a point is represented by an ordered pair of numbers (x, y).

A postulate, also known as an axiom, is a statement that is assumed to be true without proof. Postulates are the foundational assumptions upon which a mathematical or logical system is built. They serve as the starting points from which other truths can be logically deduced.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, if a number is prime, it cannot be factored into smaller integers. The first few prime numbers are 2, 3, 5, 7, 11, and 13.

A quadratic equation is a type of polynomial equation of degree 2, which means the highest power of the variable is two.

Quaternions are a four-dimension number system that can be used to elegantly represent rotations and orientations.

A radian angle is measured by the ratio of the angle's arc length over the radius of a circle. A full rotation in radians is equal to τ (tau) radians.

A random variable represents an event whose outcome is unknown. Random variables are fundamental in the study of probability and statistics, as they provide a mathematical framework for analyzing and making predictions about random processes.

The range of a function is the set of all possible output values generated by the function for a given domain. It is a measure of how the output values of a function are distributed and can be used to analyze the behavior of the function and its applications in various contexts.

A reflex angle is an angle whose measure is greater than 180 degrees but less than 360 degrees.

A right triangle (or right-angled triangle) is a triangle in which one of the angles is a right angle (90 degrees). The side opposite the right angle is called the hypotenuse, and it is the longest side. The other two sides are known as the adjacent and opposite sides, relative to the non-right angle being referenced.

A sequence is an ordered list of numbers (also called terms) that often follow a specific pattern or rule. Each term in the sequence has a unique position denoted by a positive integer, usually represented by the variable n.

A series is the sum of the terms of a sequence. It can be finite or infinite, depending on the underlying sequence. In calculus, series are used to approximate functions, study convergence and divergence, and understand the behavior of infinite sums.

A set in mathematics is a collection of distinct objects, considered as an object in its own right. Sets are one of the fundamental concepts in mathematics.

The set of complex numbers contains all possible complex numbers. Each complex number has a real part and an complex part.

The set of integers, denoted as ℤ, includes all positive and negative whole numbers, along with zero. For example, the numbers -2, 0 and 3 are all integers, but numbers like 1/2 or the square root of 2 are not.

The set of natural numbers, denoted as ℕ, includes all positive integers starting from 0. In some definitions, the set starts from 1 instead of 0.

A set of numbers is a collection of numbers grouped together based on specific properties. Common sets of numbers include the natural numbers, integers, rational numbers, real numbers, and complex numbers.

The set of rational numbers, denoted as ℚ, can be defined by the quotient of two numbers belonging to the set of integers, where the divisor is non-zero.

The set of real numbers, denoted as ℝ, includes all rational and irrational numbers. It represents the entire continuum of possible number values from negative infinity to positive infinity.

A sphere is a three-dimensional geometric shape that is perfectly symmetrical around its center. All points on the surface of a sphere are equidistant from its center.

Supplementary angles are a pair of angles that add up to 180 degrees. When two angles are supplementary, each angle is said to be the supplement of the other.

SVG is an XML-based vector image format for two-dimensional graphics.

In math, the term "tangent" is used in both trigonometry and geometry. In trigonometry, tangent is one of the primary trigonometric functions. In geometry, a tangent refers to a straight line or plane that touches a curve at a single point without crossing through it at that point.

TeX is a popular typesetting system for authoring technical documents and math expressions. It allows for precise control over the layout and appearance of documents.

A theorem is a statement that has been proven to be true within the framework of a mathematical system, based on the system's axioms and previously established theorems.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. The sum of the internal angles of a triangle in Euclidean space is always 180 degrees. The study of triangles is known as trigonometry.

Unicode is a universal character encoding standard used across operating systems and the web, facilitating the representation of text for all languages.

A variable is a symbol that represents an unknown or indeterminant quantity. Variables can represent numbers, vectors, or other mathematical objects, depending on the context.

A vector is a mathematical object represented by an ordered list of numbers called components, which define its magnitude and direction in a multi-dimensional space.

Volume is a measure of the amount of space that an object or substance occupies. In mathematics, especially in solid geometry, it is used to determine the capacity or space within a 3-dimensional object.

In math, a wave is typically represented as a periodic oscillation that can be described using functions like the sine or cosine. Waves are characterized by parameters such as amplitude, frequency, wavelength, and phase shift, and they form the foundation of wave mechanics and Fourier analysis.

The x-intercept of a graph is the point(s) at which the graph intersects the x-axis. In other words, it is the value of x when the function or equation's output (y-value) is zero.