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Euler's formula i e 1 Leonhard Euler Euler was one of the most popular mathematicians of all time. He made important breakthroughs in fields such as calculus and graph theory. e E is a constant value that is the base of a natural logarithm. Its exact value to 20 decimal places is 2.71828 18284 59045 23536... When differentiated or integrated the value of e to the power of x will remain the same. i i is an imaginary number that allows the real number system to be extended into the complex number system. It is better known as the square root of –1. i is one of few values that when squared will equal negative 1 Pi is one of the most popular numbers used in mathematics, particularly when looking at circles. Its main use is showing the ratio of the circumference of a circle to its diameter. The value of pi to 20 decimal places is 3.14159 26535 89793 23846, but it can be calculated to over a trillion decimal places. i e 1 We know that: eix cos x i sin x Let: x i e We get: cos i sin Since:cos 1 and:sin 0 We get: ei 1 i e 1 The expantion of e is: x 2 x3 x 4 e 1 x ... 2! 3! 4! x Let: x i 2 3 4 ( i ) ( i ) ( i ) ... We get ei 1 i 2! 3! 4! 2 3 4 i i Which is: e 1 i ... 2! 3!3 45! 7 Separate to get: 3 5 i e i( 7 3! 5! Because:i( 3! 5! 7! ...) 0 And: We get ei 1 ...) (1 2 4 6 7! 2! 4! 6! 2 4 6 (1 ...) 1 2! 4! 6! ...) i e 1 Proof that there is a God, and that Matthew James Leech is WRONG!!!!