Alex's Adventures in Numberland - Alex Bellos [176]
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 3x.
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 = 10b, 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