# Simple Maths Dictionary

### Here, in alphabetical order, are just some of the simpler mathematical words and expressions for reference.

Algorithm
A set of instructions used to solve a problem or obtain a desired result.

Acceleration
The rate of change of velocity over time.

Acute Angle
An angle that measures less than 90°.

Algebra
The mathematics of working with variables.

Area
Area of a circle = π
Area of a rectangle = height x width
Area of a triangle = half base x height

Arithmetic
Calculations involving numbers. This typically involves the basic operations addition, subtraction, multiplication, division, and exponents. Some people also consider roots, logarithms, calculations modulo n, and other more sophisticated operations to be arithmetic as well.

Average
This almost always refers to the arithmetic mean. In general, however, the average could be any single number that represents the centre of a set of values.

Base of a Triangle
The side of a triangle which is perpendicular to the altitude.

Calculus
The branch of mathematics dealing with limits, derivatives, definite integrals, indefinite integrals, and power series.
Common problems from calculus include finding the slope of a curve, finding extrema, finding the instantaneous rate of change of a function, finding the area under a curve, and finding volumes by parallel cross-sections.

Cardinal Numbers
The numbers 1, 2, 3, . . . as well as some types of infinity. Cardinal numbers are used to describe the number of elements in either finite or infinite sets.

Circumference
A complete circular arc. Circumference also means the distance around the the outside of a circle.

Compound Fraction
Complex Fraction
A fraction which has, as part of its numerator and/or denominator, at least one other fraction.

Compound Interest
A method of computing interest in which interest is computed from the up-to-date balance. That is, interest is earned on the interest and not just on original balance.

Constant
As a noun, a term or expression with no variables. Also, a term or expression for which any variables cancel out. For example, –42 is a constant. So is 3x + 5 – 3x, which simplifies to just 5.
As an adjective, constant means the same as fixed. That is, not changing or moving.

cos
Cos
ine
The trig function cosine, which is written cos θ. For acute angles, cos θ can be found by the SOHCAHTOA definition.

Denominator
The bottom part of a fraction.

Diameter of a Circle or Sphere
A line segment between two points on the circle or sphere which passes through the centre. The word diameter also refers to the length of this line segment.

Difference
The result of subtracting two numbers or expressions. For example, the difference between 7 and 12 is 12 – 7, which equals 5.

Dimensions
On the most basic level, this term refers to the measurements describing the size of an object. For example, length and width are the dimensions of a rectangle.

Equilateral Triangle
A triangle with three congruent sides. Note: The angles of an equilateral triangle are each 60°.

Even Number
An integer that is a multiple of 2.
The even numbers are { . . . , –4, –2, 0, 2, 4, 6, . . . }.

Fibonacci Sequence
The sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . for which the next term is found by adding the previous two terms. This sequence is encountered in many settings, from population models to botany.
Note: The sequence of ratios of consecutive terms has the Golden Mean as its limit.

Formula
An expression used to calculate a desired result, such as a formula to find volume or a formula to count combinations. Formulas can also be equations involving numbers and/or variables, such as Euler's formula.

Fraction
A ratio of numbers or variables. Fractions may not have denominator 0.

Function
A relation for which each element of the domain corresponds to exactly one element of the range.

Golden Mean/Golden Ratio
The number (1+sq. root of five divided by 2), or about 1.61803. The Golden Mean arises in many settings, particularly in connection with the Fibonacci sequence. Note: The reciprocal of the Golden Mean is about 0.6103, so the Golden Mean equals its reciprocal plus one. It is also a root of x2 – x – 1 = 0.
Note: The Greek letter phi, φ, is often used as a symbol for the Golden Mean. Occasionally the Greek letter tau, τ, is used as well.

Golden Rectangle
A rectangle which has its ratio of length to width equal to the Golden Mean. This is supposedly the rectangle which is most pleasing to the eye.

Googol
The number 10100. This number can be written as a 1 followed by 100 zeros.

Googolplex
The number 10googol, or 1 followed by a googol number of zeros. This is reputed to be the largest number with a name.
Note: This can also be written 10(10^100).

Gravity
The force which pulls masses towards each other. In high school maths, we see this most often as the force which pulls objects downwards. Note: The force of gravity between two objects is jointly proportional to the mass of each object and inversely proportional to the square of the distance between between their centres of mass.

Half-Life
For a substance decaying exponentially, the amount of time it takes for the amount of the substance to diminish by half.

Hypotenuse
The side of a right triangle opposite the right angle. Note: The hypotenuse is the longest side of a right triangle.

Infinity
A "number" which indicates a quantity, size, or magnitude that is larger than any real number. The number infinity is written as a sideways eight: ∞. Negative infinity is written –∞.
Note: Neither ∞ nor –∞ is a real number.

Integers
All positive and negative whole numbers (including zero).

Interest
The process by which an amount of money increases over time. With interest, a fixed percentage of the money is added at regular time intervals

Isosceles Triangle
A triangle with two sides that are the same length. Formally, an isosceles triangle is a triangle with at least two congruent sides.

Logarithm
The logarithm base b of a number x is the power to which b must be raised in order to equal x. This is written logb x. For example, log2 8 equals 3 since 23 = 8.

Mean
Another word for average. Mean almost always refers to arithmetic mean. In certain contexts, however, it could refer to the geometric mean, harmonic mean, or root mean square.

Natural Numbers/Counting Numbers
The numbers used for counting. That is, the numbers 1, 2, 3, 4, etc.

Numerator
The top part of a fraction.

Odd Number
An integer that is not a multiple of 2.
The odd numbers are { . . . , –3, –1, 1, 3, 5, . . . }

Ordinal Numbers
Numerical words that indicate order. The ordinal numbers are: first, second, third, fourth, etc.

Perfect Number
A number n for which the sum of all the positive integer factors of n which are less than n add up to n.
For example, 6 and 28 are perfect numbers. The number 6 has factors 1, 2, and 3, and 1 + 2 + 3 = 6. The number 28 has factors 1, 2, 4, 7, and 14, and 1 + 2 + 4 + 7 + 14 = 28.

Perfect Square
Any number that is the square of a rational number. For example, 0, 1, 4, 9, 16, 25, etc. are all perfect squares.

Power
The result of raising a base to an exponent. For example, 8 is a power of 2 since 8 is 23.

Prime Number
A positive integer which has only 1 and the number itself as factors. For example, 2, 3, 5, 7, 11, 13, etc. are all primes. By convention, the number 1 is not prime.

Product
The result of multiplying a set of numbers or expressions.

Proper Fraction
A fraction with a smaller numerator than denominator. For example, 3/5 is a proper fraction.

Pythagorean Theorem
An equation relating the lengths of the sides of a right triangle. The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

An equation includes only second degree polynomials. Some examples are y = 3x2 – 5x2 + 1, x2 + 5xy + y2 = 1, and 1.6a2 +5.9a – 3.14 = 0.

Note: When there is only one variable, a quadratic equation can be expressed in the form ax2 + bx + c = 0 where a, b, and c are all constants.

Quotient
The result of dividing two numbers or expressions. For example, the 40 divided by 5 has a quotient of 8.
Note: 43 divided by 5 has a quotient of 8 and a remainder of 3.

Reduce a Fraction
Simplify. That is, cancel out all common factors in the numerator and denominator until no common factors remain.

sin
Sine

The trig function sine, written sin θ. For acute angles, sin θ can be found by the SOHCAHTOA definition.

Simple Interest
A method of computing interest. Interest is computed from the (original) principle alone, no matter how much money has accrued so far.

SOHCATOA
A way of remembering how to compute the sine, cosine, and tangent of an angle.

SOH stands for Sine equals Opposite over Hypotenuse.
CAH stands for Cosine equals Adjacent over Hypotenuse.
TOA stands for Tangent equals Opposite over Adjacent.

Square Root
Represented by this symbol √ a square root of any particular number is a number, which when multiplied by itself, will produce the given number. NB as two negative numbers multiplied together will result in a positive answer it is important to realise that square roots can be positive or negative numbers. Thus the square root of 9 (√9) is either +3 or −3.

Sum
The result of adding a set of numbers or algebraic expressions.

tan
Tangent
The trig function tangent, written tan θ.
tan θ equals sinθ/cosθ For acute angles, tan θ can be found by the SOHCAHTOA.

Variable
A quantity that can change, or that may take on different values. Variable also refers to a letter or symbol representing such a quantity.

Whole Numbers
Non-negative Integers
The numbers 0, 1, 2, 3, 4, 5, etc.

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