Algebraic Numbers

Algebraic Numbers is in Real Numbers.

Real Numbers can be either Algebraic Numbers or Transcendental Number.

Culture, General Things, Mathematics, Real Numbers, Algebraic Numbers, Irrational Number

Irrational Number. An Irrational Number is a number that cannot be expressed as a Fraction.

Constructable Numbers

Constructable Numbers are numbers that can be derived using a straight edge and a compass.

Golden Ratio

The Golden Ratio, also known as the Golden Mean and Golden Section, is 1.618033... It is the solution to the equation x^2 - x - 1 = 0, or ( a + b ) / a = a / b.

The Golden Ratio is usually represented by the Greek Letter phi φ.

The Fibaonacci Series converges on the Golden Ratio.

The formula ( 1 + SQRT(5) ) / 2 is the Golden Ratio.

Square Root of 2

Square Root of 2, or 2^(1/2) being the length of the diagonal of a square with sides of length 1. It is 1.4142135623...

99/70 = 1.4142857 approximates to the Square Root of 2.

Non-Constructable Numbers

Non-Constructable Numbers are the solution to algebraic equations with a cube root of higher eg 2^(1/3).

Culture, General Things, Mathematics, Real Numbers, Algebraic Numbers, Rational Number

Fractions

Fractions are an Integer divided by an Integer eg 1/2, 5/13, 241/98.

Rational Number. A Rational Number is a number that can be expressed as a Fraction of two Integers. Integers are Fractions with a divisor of 1.

Irrational Number. An Irrational Number is a number that cannot be expressed as a Fraction.

Integers

Integers aka whole numbers. Fractions with a divisor of 1.

Prime Number

Prime Number. A Prime Number is an Integer that is only divisible by 1 and itself with the Remainder ie. 1, 2, 3, 5, 7, 11, 13, 17, 19, ...

Fermat Prime

Fermat Prime. A Prime Number that is a solution to 2^2^N + 1 eg 3, 5, 17, 65537, 4294967297, 18446744073709551617

2 ^ 2 ^ 0 + 1 = 3

2 ^ 2 ^ 1 + 1 = 5

2 ^ 2 ^ 2 + 1 = 17

With the exeception of the first and second terms Germat Primes always end in 7.

Mersenne Prime

Mersenne Prime. A Mersenne Prime is a prime number that is one less than a power of two. Mersenne Primes do not include all numbers that are one less than a power of two eg 16 - 1 = 15 which is divisible by 1, 3 and 5.