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# Présentation - Leonhard Euler

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### Présentation - Leonhard Euler

1. 1. Leonhard Euler (1707-1783)
2. 2. Introduction → Introduction → His life → His most important works → Conclusion
3. 3. His life Born in Basel in 1707 At 16 : Master of Philosophy Received lessons from Bernouilli In 1727 he went to St Petersburg
4. 4. His life 1731 : professor of physics 1733 : head of the mathematics department 1741 : he went to Berlin Academy 1766 : came back in St Petersburg He died in 1783
5. 5. Mathematical notations The concept of a function, notation f(x) The letter e ''Euler's number'' use to define the Exponential function : ex The greek letter Ʃ for summations The famous greek letter π The letter i to denote the imaginary unit
6. 6. Analysis n x ∞ x e =∑ n =0 n ! ∞ 1 ² ∑ n2 = 6 '' The Basel Problem '' n=1 i e =cos i sin  '' The Euler's formula '' i e 1=0 '' The Euler's identity ''
7. 7. Number Theory The infinitude of prime numbers The sum of the reciprocals of the primes diverges The totient function : φ(n) The Euler's theorem 231 − 1 = 2,147,483,647 is a Mersenne prime
8. 8. Euler's circle
9. 9. Euler's line
10. 10. Graph theory V–E+F=1
11. 11. Conclusion
12. 12. http://scienceworld.wolfram.com/biography/Euler.html http://www.maths.tcd.ie/pub/HistMath/People/Euler/Ro http://www.pdmi.ras.ru/EIMI/EulerBio.html http://www-history.mcs.st- and.ac.uk/Biographies/Euler.html http://en.wikipedia.org/wiki/Leonhard_Euler