Leonhard euler

Lenohard euler life and contribution

1. Leonhard Euler 15 April 1707 - 18 September 1783

2. His life Leonhard Euler was one of the giants of 18th Century mathematics. He was born in Basel, Switzerland, and he studied for a while under  Johann Bernoulli  at Basel University. He is said to have produced on average one mathematical paper every week. He was a revolutionary thinker in the fields of geometry, trigonometry, calculus, differential equations, number theory and notational systems. In 1738, he became almost blind in his right eye. Euler, working on the day of his passing, suffered from a brain hemorrhage and died during the night of September 18, 1783, in St. Petersburg. Euler's legacy has been enormous in terms of shaping the modern playing field of mathematics and engineering

3. Contributions

4. Mathematical notation He introduced the concept of a function and was the first to write to denote the function applied to the argument . He also introduced the modern notation for the trigonometric functions, the letter for the base of the natural logarithm, the letter for summations and the letter ‘ ’ to denote the imaginary unit.  

5. Euler's Formula about Geometry For any polyhedron  that doesn't intersect itself,  the Number of Faces plus the  Number of Vertices  (corner points) minus the  Number of Edges always equals 2 This can be written:  F + V − E = 2 Try it on the cube: A cube has 6 Faces, 8 Vertices, and 12 Edges, so: 6 + 8 − 12 =  2

6. Euler's Formula about complex numbers A mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. e i x  = cos x +  i  sin x e = base of the natural logarithm i = imaginary unit x = the angle in radians Example: when x = 1.1 e i x  = cos x +  i  sin x e 1.1i  = cos 1.1 +  i  sin 1.1 e 1.1i  = 0.45 + 0.89  i  

7. Euler’s Theorem for Homogenous function If is a homogeneous function of degree then  

8. Euler’s Totient Theorem :- It states that if and are co-prime positive integers, then Where euler's totient function    

9. Thank You