Math Glossary

Math Glossary

Math Glossary of Mathematical Terms & Definition

 

A 

Math Glossary

1. Absolute Value: The distance of a number from zero on the number line. It is always non-negative.

2. Abundance: The sum of a number’s proper divisors is greater than the number itself.

3. Acceleration: The rate of change of velocity with respect to time.

4. Acute Angle: An angle that measures less than 90 degrees.

5. Addition: A basic arithmetic operation that combines two or more numbers to give a total or sum.

6. Algebra: A branch of mathematics that deals with symbols and rules for manipulating those symbols to solve equations and study relationships.

7. Algorithm: A step-by-step procedure or set of rules for solving a problem or completing a task.

8. Alternate Interior Angles: Pairs of angles on opposite sides of a transversal that are inside the parallel lines and equal in measure.

9. Amplitude: The maximum value of a periodic function.

10. Angle: A figure formed by two rays that share a common endpoint (vertex).

11. Arc: A portion of a circle’s circumference.

12. Area: The measure of the amount of space enclosed by a two-dimensional shape.

13. Arithmetic: The branch of mathematics that deals with basic operations such as addition, subtraction, multiplication, and division.

14. Array: A rectangular arrangement of objects or numbers in rows and columns.

15. Associative Property: The property that states that the grouping of numbers in an operation does not affect the result (e.g., (a + b) + c = a + (b + c)).

16. Axis: A reference line used in coordinate geometry to locate points in space. In a Cartesian coordinate system, there are usually two axes: x-axis and y-axis.

B 

Math Glossary

17. Base: The number that is raised to a power in an exponential expression.

18. Binary: A numbering system that uses only two symbols, typically 0 and 1.

19. Binomial: An algebraic expression with two terms.

20. Bisect: To divide into two equal parts.

21. Calculus: A branch of mathematics that deals with rates of change and accumulation.

22. Cardinality: The number of elements in a set.

23. Cartesian Coordinates: A system for representing points in space using a pair of numerical values (x, y) that correspond to distances along two perpendicular lines (axes).

24. Circumference: The distance around the boundary of a circle.

25. Coefficient: A constant multiplier in an algebraic expression.

26. Commutative Property: The property that states that the order of numbers in an operation does not affect the result (e.g., a + b = b + a).

27. Complement: The set of elements that do not belong to a given set.

28. Composite Number: A positive integer greater than 1 that has more factors than just 1 and itself.

29. Concave: Curved inward, like the interior of a bowl.

30. Congruent: Having the same shape and size.

31. Conic Section: A curve that is formed by the intersection of a plane and a cone. Types include circles, ellipses, parabolas, and hyperbolas.

32. Conjecture: A mathematical statement that is believed to be true but has not been proven.

33. Constant: A value that does not change in a given context or situation.

34. Continuity: The property of a function that describes how it is connected over its entire domain.

35. Coordinate Plane: A two-dimensional plane formed by two perpendicular number lines (axes).

36. Counting Numbers: The set of positive integers (1, 2, 3, …).

37. Cube: A three-dimensional shape with six square faces, all of equal size.

38. Cylinder: A three-dimensional shape with two parallel circular bases connected by a curved surface.

D 

Math Glossary

39. Decimal: A number expressed in base-10 notation, with a decimal point separating the whole part from the fractional part.

40. Decompose: To break down a number, expression, or shape into simpler components.

41. Degree: The measure of the size of an angle in degrees, or the highest power of a variable in a polynomial.

42. Denominator: The bottom number in a fraction that represents the total number of equal parts in the whole.

43. Dependent Variable: In a mathematical relationship, the variable whose value depends on the value of another variable.

44. Derivative: The rate of change of a function with respect to its independent variable.

45. Diagonal: A line segment connecting two nonadjacent vertices of a polygon.

46. Diameter: A line segment that passes through the center of a circle and connects two points on its boundary.

47. Difference: The result of subtracting one number from another.

48. Digital Root: The single-digit result obtained by repeatedly summing the digits of a number.

49. Dilation: A transformation that changes the size of a figure but not its shape.

50. Dimension: The measure of the size of a space, often expressed as length, width, and height.

51. Distributive Property: The property that relates addition and multiplication, usually expressed as a(b + c) = ab + ac.

52. Dividend: The number being divided in a division operation.

53. Divisor: The number by which the dividend is divided in a division operation.

54. Domain: The set of all possible input values for which a function is defined.

E

39. Ellipse: A closed curve formed by the intersection of a cone and a plane, where the sum of the distances from any point on the curve to two fixed points (foci) is constant.

40. Empty Set: The set with no elements, denoted by ∅ or {}.

41. Equation: A mathematical statement that asserts the equality of two expressions.

42. Equilateral Triangle: A triangle with all three sides of equal length.

43. Equivalent Fractions: Fractions that represent the same part-to-whole relationship.

44. Estimate: An approximate calculation of a value based on available information.

45. Even Number: An integer that is divisible by 2.

46. Exponent: The number that indicates how many times a base number should be multiplied by itself.

47. Expression: A mathematical phrase that combines numbers, variables, and operations.

F 

Math Glossary

64. Factor: A number or expression that divides another number or expression evenly.

65. Fibonacci Sequence: A sequence of numbers where each number is the sum of the two preceding ones, starting with 0 and 1 (0, 1, 1, 2, 3, 5, 8, …).

66. Finite: Having an end or limit; not infinite.

67. Fluxion: An early term for derivative, used by Isaac Newton.

68. Fraction: A number that represents a part of a whole, consisting of a numerator and a denominator.

69. Function: A relation that assigns each input value (domain) to exactly one output value (range).

70. Fundamental Theorem of Calculus: States the connection between differentiation and integration and is a cornerstone of calculus.

G 

Math Glossary

71. Geometric Mean: The mean of a set of numbers obtained by multiplying all the values together and taking the nth root, where n is the number of values.

72. Geometric Progression (Geometric Sequence): A sequence of numbers where each term is found by multiplying the previous term by a constant ratio.

73. Geometry: The branch of mathematics that deals with shapes, sizes, properties of space, and relative positions of objects.

74. Golden Ratio: A mathematical constant, often denoted by the Greek letter phi (φ), equal to approximately 1.61803398875.

75. Graph: A visual representation of data, equations, or functions using points, lines, curves, and other geometric elements.

76. Greater Than: A comparison between two values where one is larger than the other (symbol: >).

77. Grouping Symbols: Parentheses (), brackets [], and braces {} used to indicate the order of operations in an expression.

78. Heron’s Formula: A formula for finding the area of a triangle when the lengths of its sides are known.

79. Hyperbola: A conic section defined as the set of points where the difference of the distances from two fixed points (foci) is constant.

I 

Math Glossary

80. Identity Property: The property that states that a number is unchanged when an operation is performed on it, such as a + 0 = a.

81. Imaginary Number: A number that is the square root of a negative real number, often denoted by the letter i.

82. Improper Fraction: A fraction where the numerator is equal to or greater than the denominator.

83. Inequality: A mathematical statement that compares two expressions, showing that one is greater than, less than, or equal to the other.

84. Infinite: Having no end or limit.

85. Integer: A whole number that can be positive, negative, or zero.

86. Integral: The process of finding the area under a curve or the accumulation of quantities.

87. Intercept: The point where a graph crosses an axis.

88. Intersect: To meet or cross at a point.

89. Inverse: A mathematical operation that undoes another operation.

90. Irrational Number: A number that cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal expansion.

91. Isosceles Triangle: A triangle with at least two sides of equal length.

J

92. Joint Variation: A type of variation in which a quantity varies directly with two or more variables and inversely with another variable.

K

93. Knot Theory: A branch of topology that studies the properties of mathematical knots and their spatial relationships.

L 

Math Glossary

94. Least Common Denominator (LCD): The smallest multiple that two or more denominators have in common.

95. Least Common Multiple (LCM): The smallest multiple that two or more numbers have in common.

96. Limit: The value that a function approaches as its input gets closer and closer to a certain value.

97. Line: A straight path that extends infinitely in both directions.

98. Line Segment: A portion of a line with two endpoints.

99. Linear Equation: An equation of the form ax + b = 0, where x is a variable and a and b are constants.

100. Logarithm: The exponent to which a given base must be raised to obtain a specific number.

101. Magnitude: The size or length of a vector or quantity.

102. Manipulate: To change or rearrange mathematical expressions or objects.

103. Matrix: A rectangular array of numbers, symbols, or expressions arranged in rows and columns.

104. Mean: The average of a set of numbers, obtained by summing the values and dividing by the count.

105. Median: The middle value in a set of numbers when they are arranged in order.

106. Midpoint: The point that divides a line segment into two equal parts.

107. Minuend: The number from which another number is subtracted.

108. Mode: The value that appears most frequently in a set of numbers.

109. Modulus: The absolute value or magnitude of a complex number.

110. Monomial: An algebraic expression consisting of a single term.

111. Multiplication: A basic arithmetic operation that combines two or more numbers to give a product.

112. Multiplicative Identity: The property that states that any number multiplied by 1 remains unchanged.

113. Multiplicative Inverse: The reciprocal of a number, which when multiplied by the number gives a product of 1.

N

94. Natural Numbers: The set of positive integers (1, 2, 3, …).

95. Negative Number: A number less than zero.

96. Net: A two-dimensional representation of a three-dimensional object that can be folded to form the object.

97. Nonagon: A polygon with nine sides.

98. Numerator: The top number in a fraction that represents the part of the whole.

99. Number Line: A visual representation of numbers placed on a straight line.

100. Numeric Expression: An expression that contains numbers and operations, but no variables.

O  

Math Glossary

121. Oblique Triangle: A triangle that is not a right triangle.

122. Obtuse Angle: An angle that measures more than 90 degrees but less than 180 degrees.

123. Octagon: A polygon with eight sides.

124. Odd Number: An integer that is not divisible by 2.

125. Operation: A mathematical process or procedure, such as addition, subtraction, multiplication, or division.

126. Order of Operations: A set of rules that dictate the sequence in which calculations are performed in a mathematical expression.

127. Ordinal Numbers: Numbers that represent position or rank, such as first, second, third, etc.

128. Origin: The point (0, 0) on a coordinate plane.

P 

Math Glossary

129. Parabola: A U-shaped curve formed by the graph of a quadratic function.

130. Parallel Lines: Lines in the same plane that never intersect.

131. Parallelogram: A quadrilateral with opposite sides that are parallel and equal in length.

132. Percentage: A proportion expressed as a fraction of 100.

133. Perimeter: The distance around the boundary of a two-dimensional shape.

134. Perpendicular Lines: Lines that intersect at a right angle.

135. Pi (π): A mathematical constant representing the ratio of a circle’s circumference to its diameter, approximately 3.14159.

136. Place Value: The value of a digit in a number based on its position.

137. Point: A specific location in space, usually represented by a dot.

138. Polygon: A closed shape with straight sides and angles.

139. Polynomial: An algebraic expression consisting of one or more terms, each with a variable raised to a non-negative integer exponent.

140. Positive Number: A number greater than zero.

141. Power: An expression that indicates how many times a number (base) should be multiplied by itself.

142. Prime Factorization: The expression of a composite number as a product of prime numbers.

143. Prime Number: A natural number greater than 1 that has no positive divisors other than 1 and itself.

144. Prism: A three-dimensional shape with two parallel and congruent polygonal bases connected by rectangular or parallelogram faces.

145. Probability: The likelihood of an event occurring, often expressed as a fraction or percentage.

146. Product: The result of multiplying two or more numbers.

147. Proportional Relationship: A relationship between two quantities in which their ratios remain constant.

148. Pyramid: A three-dimensional shape with a polygonal base and triangular faces that converge at a single vertex.

Q 

Math Glossary

149. Quadrant: One of the four sections into which a coordinate plane is divided by the x-axis and y-axis.

150. Quadratic Equation: A polynomial equation of the second degree, usually written in the form ax² + bx + c = 0.

151. Quadrilateral: A polygon with four sides.

152. Quotient: The result of dividing one number by another.

R 

Math Glossary

153. Radius: A line segment that connects the center of a circle to a point on its boundary.

154. Range: The set of all possible output values of a function.

155. Ratio: The quantitative relationship between two amounts, often expressed as a fraction or a proportion.

156. Rational Number: A number that can be expressed as a fraction of two integers.

157. Real Numbers: The set of all rational and irrational numbers.

158. Reciprocal: The multiplicative inverse of a number, denoted by 1/x.

159. Rectangle: A quadrilateral with four right angles.

160. Rectangular Prism: A three-dimensional shape with six rectangular faces.

161. Reflection: A transformation that “flips” a figure over a line to create a mirror image.

162. Reflex Angle: An angle that measures more than 180 degrees but less than 360 degrees.

163. Regrouping: The process of rearranging numbers when performing addition or subtraction.

164. Relation: A set of ordered pairs that establishes a connection between two sets of data.

165. Right Angle: An angle that measures exactly 90 degrees.

166. Right Triangle: A triangle that has one angle equal to 90 degrees.

167. Root: A value that, when substituted into a function, makes the function equal to zero.

168. Rotation: A transformation that turns a figure around a fixed point.

169. Round: To approximate a number to a specified place value.

S 

Math Glossary

170. Scale Factor: The ratio of the lengths of corresponding sides in similar figures.

171. Scientific Notation: A way to represent very large or very small numbers using powers of 10.

172. Secant: A line that intersects a curve at two or more points.

173. Segment: A part of a line with two endpoints.

174. Sequence: An ordered list of numbers.

175. Set: A collection of distinct objects.

176. Similar Figures: Figures that have the same shape but may have different sizes.

177. Sine: A trigonometric function that represents the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse.

178. Slope: The measure of how steep a line is, calculated as the change in vertical position divided by the change in horizontal position.

179. Solid: A three-dimensional object with length, width, and height.

180. Sphere: A three-dimensional shape in which all points on the surface are equidistant from the center.

181. Square: A quadrilateral with four sides of equal length and four right angles.

182. Square Root: A value that, when multiplied by itself, gives the original number.

183. Subtraction: A basic arithmetic operation that finds the difference between two numbers.

184. Supplementary Angles: Pairs of angles whose measures add up to 180 degrees.

185. Surface Area: The total area of all the faces of a three-dimensional shape.

T 

Math Glossary

186. Tangent: A line that touches a curve or surface at a single point, without crossing it.

187. Term: A single number, variable, or product in an algebraic expression.

188. Tessellation: The repeated use of a single shape to cover a plane without gaps or overlaps.

189. Tetrahedron: A three-dimensional shape with four triangular faces.

190. Theorem: A statement that can be proven to be true using established mathematical principles.

191. Three-Dimensional (3D): Having length, width, and height.

192. Transformation: A change in the position, size, or shape of a figure.

193. Transversal: A line that intersects two or more other lines.

194. Trigonometry: The branch of mathematics that deals with the relationships between the angles and sides of triangles.

195. Two-Dimensional (2D): Having length and width but no height.

U

196. Undefined: A mathematical expression that does not have a valid value or result.

197. Union: The combination of two or more sets, denoted by ∪.

198. Unit: A standard quantity used to measure other quantities.

199. Unit Circle: A circle with a radius of 1 unit, often used to define trigonometric functions.

V

 

200. Variable: A symbol that represents an unknown quantity in mathematical expressions or equations.

201. Vertex (Vertices): A point where two or more line segments or rays meet to form an angle.

202. Volume: The amount of space occupied by a three-dimensional shape.

W

203. Whole Number: A non-negative integer (0 and positive integers).

204. X-Axis: The horizontal reference line in a Cartesian coordinate system.

205. Y-Axis: The vertical reference line in a Cartesian coordinate system.

206. Zero: The integer that represents the absence of quantity or value.