Glossary

Algorithm: a set of rules or instructions designed to solve a problem.

 

Ambigram: a word (or set of words) written in such a way as to conceal other words, often the same word (or set of words) written upside-down.

 

Amicable number: two numbers are amicable if the factors of one add up to the other and vice versa.

 

Axiom: a statement that is accepted without proof, usually because it is self-evident, and used as a foundation of a logical system.

 

Base: in a number system, the base is the size of the number-grouping which, when using Arabic numerals, is equal to the number of different digits allowed in the system. Binary, using 0 and 1, is base two, while decimal, using 0 to 9, is base ten.

 

Cardinality: the size of a set.

 

Circumference: the perimeter of a circle.

 

Combinatorics: the study of combinations and permutations.

 

Constant: a fixed value.

 

Continuum: the points on a continuous line.

 

Convergent series: an infinite series that adds up to a finite number.

 

Correlation: a measure of the interdependence of two variables.

 

Countable infinity: an infinite set, the members of which can be put in a one-to-one correspondence with the natural numbers.

 

Cubic equation: an equation of the form ax³ + bx² + cx + d = 0, where a, b, c and d are constants and a is non-zero.

 

Curvature: a property of space that can be determined by the behaviour of triangles or parallel lines.

 

Decimal fraction: a fraction when written with a decimal point, so 1.5 is the decimal fraction equal to .

 

Denominator: the number beneath the line in a fraction.

 

Diameter: the width of a circle.

 

Distribution: a spread of possible outcomes and their likelihood of occurring.

 

Divergent series: an infinite series that does not add up to a finite number.

 

Divisor: a natural number that divides into another number with no remainder; so 5 is a divisor of 20.

 

Dyscalculia: a condition affecting one’s ability to grasp numbers.

 

Edge: the chance of winning a gamble minus the chance of losing.

 

Egyptian triangle: a triangle whose sides have the ratios 3:4:5.

 

Expected value: the theoretical value of how much you can expect to win or lose in a bet.

 

Exponent: the power of a number, written as a raised symbol, such as the x in 3^x.

 

Factor: a divisor of a given number.

 

Factorize: to break a number down into its factors, usually just the ones that are prime numbers.

 

Fibonacci number: a number in the Fibonacci series, which begins 1, 1, 2, 3, 5, 8, 13…

 

Gambler’s fallacy: the false idea that random outcomes are not random.

 

Gambler’s ruin: the inevitability of bankruptcy if you gamble for long enough.

 

Gaussian distribution: the normal distribution.

 

Geometric progression: a sequence of numbers in which each new term is calculated by multiplying the previous term by a fixed number.

 

Hyperbolic plane: an infinitely large surface with negative curvature.

 

Hypotenuse: the side of a right-angled triangle opposite the right angle.

 

Infinite series: a series with an infinite number of terms.

 

Integer: a number that is one of the natural numbers, negative natural numbers or zero.

 

Inversion: the same thing as an ambigram.

 

Irrational number: a number that cannot be expressed as a fraction.

 

Latin square: a square grid where every element occurs only once in each row and column.

 

Law of large numbers: the rule that probability works out in the long run, in that the more examples of a random event you have (such as the flipping of a coin), the closer the actual results will be to the expected results.

 

Law of very large numbers: the rule that if the sample is large enough, then any result may occur no matter how unlikely.

 

Logarithm: if a = 10^b, then the logarithm of a is b, written log a = b.

 

Magic square: a square grid containing consecutive numbers from 1 such that the sum of all rows, columns and diagonals are equal.

 

Mersenne prime: a prime number that can be expressed as 2n – 1.

 

Natural number: any whole number that can be reached counting upwards from 1.

 

Normal distribution: the most common type of distribution, which produces the bell curve.

 

Normal number: a number whose decimal digits consist of an equal number of 0s, 1s, 2s, 3s, 4s, 5s, 6s, 7s, 8s and 9s.

 

Number line: a visual representation of numbers as points on a continuous line.

 

Numerator:the number above the line in a fraction.

 

Order of magnitude: Most commonly, the scale of a number based on the positional value of the leftmost digit of that number. So, the order of magnitude of any number between 1 and 9 is one, between 10 and 99 is two, between 100 and 999 is three, and so on.

 

Parallel: two straight lines that never meet are parallel.

 

Perfect number: a number that is equal to the sum of its divisors (excluding itself).

 

Phi: the mathematical constant, the decimal expansion of which begins 1.618…, and is also known as the golden ratio, or the divine proportion.

 

Pi: the mathematical constant, the decimal expansion of which begins 3.14159265358979323846…, and that is equal to the ratio between the circumference and the diameter of a circle.

 

Platonic solid: the five solids whose sides are all identical regular polygons; in other words, the tetrahedron, cube, octahedron, icosahedron and dodecahedron.

 

Polygon: a two-dimensional closed shape made up of a finite number of straight lines.

 

Postulate: a statement that is assumed to be true, and used as an axiom.

 

Power: an operation that determines how many times a number is to be multiplied by itself, so if 10 is to be multiplied by itself four times, one writes 10⁴ and calls this ‘ten to the power of four’. Powers are not always natural numbers, but when one talks about the ‘powers of x’ it is assumed that one is referring only to the powers of x that are.

 

Prime number: a natural number that has only two divisors, itself and 1.

 

Probability: the chance of an event taking place, expressed as a fraction between 0 and 1.

 

Quadratic equation: an equation of the form ax² + bx + c = 0, where a, b, and c are constants and a is non-zero.

 

Radius: a straight line from the centre of a circle to the circumference.

 

Randowalk: a visual interpretation of randomness, in which each random event is expressed as movement in a random direction.

 

Rational number: a number that can be expressed as a fraction.

 

Regression to the mean: the phenomenon that after extreme events less extreme ones are more likely.

 

Regular polygon: a polygon with sides of equal length and with equal internal angles.

 

Sequence: a list of numbers.

 

Series: the sum of the terms in a sequence.

 

Set: a collection of things.

 

Tessellation: an arrangement of tiles that fills a two-dimensional space completely with no overlaps.

 

Theorem: a statement that can be proved from other theorems and/or axioms.

 

Transcendental number: a number that cannot be expressed as a solution to a finite equation.

 

Uncountable infinity: an infinite set whose members cannot be put in a one-to-one correspondence with the natural numbers.

 

Unique solution: the situation when there is one and only one possible answer.

 

Variable: a quantity that can vary in value.

 

Vertex: where two lines meet to form an angle, or the angular points in a three-dimensional shape.