**Euler's Number (e)**

2.718281828459045235360287471352662497757247.....

This number is the base for natural logarithms usually shown by

*Ln*or

*e*on calculators.

^{x}e = (1 +

^{1}/

_{n})

^{n}

when n is a very large number (as close to infinity as practicable)

e = 1 +

^{1}/

_{1!}+

^{1}/

_{2!}+

^{1}/

_{3!}+

^{1}/

_{4!}+

^{1}/

_{5!}+ ....

e = (1 + n)

^{(-n)}

when n is a very small number (as close to zero as practicable)

e = ∑(

^{(2n + 2)}/

_{(2n +1)!})

(Sum from n=0 to n=infinity)

**Pi (π)**

3.141592653589793238462643383279502884197169399...

This number is used extensively in maths, physics and circles.

π =

^{4}/

_{1}-

^{4}/

_{3}+

^{4}/

_{5}-

^{4}/

_{7}+

^{4}/

_{9}-

^{4}/

_{11}+

^{4}/

_{13}-

^{4}/

_{15}....

π = 3 +

^{4}/

_{2x3x4}-

^{4}/

_{4x5x6}+

^{4}/

_{6x7x8}-

^{4}/

_{8x9x10}+

^{4}/

_{10x11x12}-

^{4}/

_{12x13x14}+

^{4}/

_{14x15x16}....

π = ∑( 16

^{(-n)}(

^{4}/

_{(8n+1)}-

^{2}/

_{(8n+4)}-

^{1}/

_{(8n+5)}-

^{1}/

_{(8n+6)}) )

**Golden Ratio Φ**

1.61803398874989484820458....

Φ =

^{(1+√5)}/

_{2}

**Euler-Mascheroni Constant γ**

0.5772156649015328606065120900824024310421593359...

γ = ∑(

^{1}/

_{n}) - Ln(n)

(Sum n=0 to n=very_large_number)

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