educ

1. Leonhard Euler
(1707-1783)

2. Introduction
→ Introduction
→ His life
→ His most important works
→ Conclusion

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. 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. 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. Analysis
ex
=∑∞ xn
n =0 n!
∑
n=1
∞
n2
=
1 𝜋²
6
'' The Basel Problem ''
ei
=cos( )+isin( )
ei𝜋
+1=0
'' The Euler's formula ''
'' The Euler's identity ''

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. Euler's circle

9. Euler's line

10. Graph theory
V – E + F = 1

11. Conclusion

12. http://scienceworld.wolfram.com/biography/Euler.html
http://www.maths.tcd.ie/pub/HistMath/People/Euler/R
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