Bernhardriemann
- 1. Bernhard Riemann 1826 -1866.By: jonathan rodriguez
- 2. Biography of Bernhard RiemannBernhard Riemann was born in 1826 and died in 1866.
- 3. He was the son of a poor country minister in northern Germany.
- 4. He studied some of Euler and Legendre while he was in secondary school.
- 5. He mastered Legendre’s treatise on Theory of Numbers in less than a week.He was a shy and modest man.
- 6. He went to University of Gottingento study and become a minister himself.
- 7. But before it was too late he realized his mistake and with his father’s permission, he switched to mathematics.
- 8. After a while he switched to University of Berlin.
- 9. Once there he learned a great deal from Dirichlet and Jacobi.
- 10. After tow years, he returned to Gottingen, where he obtained his doctor’s degree.In 1854 he was appointed as an "unpaid lecturer" which at the time was the necessary first step on the academic ladder.
- 11. Gauss died in 1855, and Dirichlet was called to Gottingen as his successor.
- 12. Dirichlet helped Riemann in every way he could and even arranged a small salary for him.
- 13. But Dirichlet died in 1859 and Riemannwas appointed as a full professor to replace him.
- 14. Riemann's lecture presented in nontechnical language a vast generalization of all known geometries, both Euclidean and non-Euclidean. This field is now called Riemannian Geometry; and apart from its great importance in pure mathematics, it turned out 60 years later to be exactly the framework for Einstein's general theory of relativity.
- 15. Like most of the great ideas of science, Riemannian geometry is quite easy to understand if we set aside the technical details and concentrate on its essential features.
- 16. Gauss had earlier discovered the intrinsic differential geometry of curved surfaces.
- 17. If a surface embedded in three dimensional space is defined parametrically by three functions x=x(u,v), y=y(u,v), and z=z(u,v), then u and v can be interpreted as the coordinates of the points on the surface.
- 18. The distance ds between any two nearby points (u,v) and (u+du,v+dv) is given by Gauss's quadratic differential form: ds = Edu^2 + 2Fdudv + Gdv^2,
- 19. Have a great summer!!!