# 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 r²

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 10^{100}. This number can be
written as a 1 followed by 100 zeros.

**Googolplex**

The number 10^{googol}, 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 log_{b}* x*.
For example, log_{2 }8 equals
3 since 2^{3} = 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 2^{3}.

**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.

**Quadratic
Equation**

An equation includes only second degree polynomials.
Some examples are *y* = 3*x*^{2} – 5*x*^{2} +
1,* x*^{2} + 5*xy* + *y*^{2} =
1, and 1.6*a*^{2} +5.9*a* – 3.14
= 0.

Note: When there is only one variable, a quadratic equation can
be expressed in
the form *ax*^{2} + *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 **S**ine equals **O**pposite
over **H**ypotenuse.

CAH stands for **C**osine equals **A**djacent
over **H**ypotenuse.

TOA stands for **T**angent equals **O**pposite
over **A**djacent.

**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.