# Culture, General Things, Mathematics, Real Numbers, 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.

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

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

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

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

Culture, General Things, Mathematics, Real Numbers, Algebraic Numbers, Irrational Number, Natural Logarithm of 2

Natural Logarithm of 2. Is the logarithm of 2 to the base of e. It is usually written as ln2. It is a Transcendental Number.

The Alternating Harmonic Series: SUM(1,INFINITY) ( (-1)**(N+1) ) / N = 1 - (1/2) + (1/3) - (1/4) + (1/5) - (1/6) + ....

Or Binary Rising Constant Factorial: SUM(1,INFINITY) 1 / ( ( 2**N ) *N) = 1/2 + 1/8 + 1/24 + 1/64 + 1/160 + 1/384 + 1/896 + ....

Or SUM(0,INFINITY) 1 / ( ( 2N + 1 ) * ( 2N + 2 ) ) = 1 / ( 4N**2 + 6N + 2 ) = 1/2 + 1/12 + 1/30 + 1/56 + 1/90 + 1/132 + 1/182 + 1/240 + ....

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

PI is the ratio of diameter and circumference of a circle. It is a Transcendental Number.

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e. Euler's Number is 2.718254. It is usually written as 'e'. It is a Transcendental Number.

Euler's Number is the number to which compounding, as in compount interest, converges.

For example, if interest is paid at 100% then after one year £1 becomes £2.

If the interest is charged at 50% twice then the interest will be ( 1 * 1.5 ) * 1.5 = 1.5**2 = 2.25

If the interest is charged at 25% four times then the interest will be ( ( ( ( 1 * 1.25 ) * 1.25 ) * 1.25 ) * 1.25 )= 1.25**4 = 2.44

If the interest is charged at 8.33% twelve times then the interest will be 1.0833**12 = 2.612

If the interest is charged at 4.2% twenty-four times year then the interest will be ( 1.042**4 ) = 2.67

If the interest is charged at 0.1% one thousand times then the interest will be ( 1.001**1000 ) = 2.72

If the interest is charged at an infinite number of times then the interest will be ( 1.00/∞ )**∞ = 2.718254... which is Euler's number.

Euler's Number is the sum of the infinite series ( 1 / n! ) ie 1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 + 1/720 + 1/5040 .... = 2.718281828.

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

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.

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.

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

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

Culture, General Things, Mathematics, Real Numbers, Algebraic Numbers, Rational Number, Integers, Prime Number, 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.

Culture, General Things, Mathematics, Real Numbers, Algebraic Numbers, Rational Number, Integers, Prime Number, 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.