Pafnouti Tchebychev

Pafnouti Lvovitch Tchebychev (ПафнутийЛьвовичЧебышёв) (May 4th 1821 with Okatovo - November 26th 1894 with Saint-Pétersbourg) Russian mathematician was a . Its name is also transliterated like Chebyshov , Chebyshev , or Tschebyscheff .

It is known for its work in the field of the Probabilité S and the Statistiques.

Tchebychev belongs to the Russian mathematical school founded under Catherine Large the by Daniel Bernoulli and Euler. In is also resulting its contemporary Lobatchevsky, initiator of the not-Euclidean Géométrie.

Tchebychev takes again the vast program initiated by Jacques Bernoulli, Abraham de Moivre and Siméon Denis Poisson to state and show in a rigorous way of the limiting theorems, i.e. to establish the asymptotic tendencies of the natural phenomena. It establishes a law of the great numbers very general and gives a news and brilliant method of demonstration based on the inequality shown by Bienaymé.

In Theory of the numbers, Tchebychev supplemented in 1848 a conjecture of Gauss relating to the rarefaction of the Prime numbers. It showed in 1850 a conjecture stated by Bertrand: “For entire N at least equal to 2, there exists a prime number between N and 2n”.

It also conceived a mechanical structure called " Horse of Tchebychev". It consists of 4 feet and a supposed plate being the back of the horse. When that the " cheval" advances, the plate remains with constant height.

After him Liapounov and Markov, its pupils, will continue his work and this Russian tradition led to Kolmogorov, founder of the contemporary probabilities.

• the inequality of Tchebychev is used to prove the weak law of the great numbers and the theorem of Bertrand-Tchebychev (1845 | 1850) mentioned above.

• the Polynomials of Tchebychev as well as the group Antifolk the Pafnouties are named in its honor.
• In electronic analogical, there exists a family of filters named “filters of Tchebychev”.

See too

• Inequality of Bienaymé-Tchebychev
• secondary Measurements