Algebraic Numbers
Algebraic Numbers is in Real Numbers.
Real Numbers can be either Algebraic Numbers or Transcendental Number.
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).
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.
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.
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.