 Special Numbers
Crib Sheets
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Euler's Number (e)
2.718 281 828 459 045 235 360 287 471 352 662 497 757 247.....
This number is the base for natural logarithms usually shown by Ln or ex on calculators.
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)
3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399...
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
1.618 033 988 749 894 848 204 58....
Φ = (1+√5)/2

Euler-Mascheroni Constant γ
0.577 215 664 901 532 860 606 512 090 082 402 431 042 159 335 9...
γ = ∑(1/n) - Ln(n)
(Sum n=0 to n=very_large_number)

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