1. Euler's formula

2. 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.

3. 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.

4. 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

5. 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.

6. We know that: Let: We get: Since:and: We get:

7. The expantion of e is: Let: We get Which is: Separate to get: Because:And: We get

8. Proof that there is a God, and that Matthew James Leech is WRONG!!!!