Édouard Lucas
Édouard Lucas | |
---|---|
Scientific career | |
Fields | Mathematics |
François Édouard Anatole Lucas (French pronunciation: [fʁɑ̃swa edwaʁ anatɔl lykɑ]; 4 April 1842 – 3 October 1891) was a French mathematician. Lucas is known for his study of the Fibonacci sequence. The related Lucas sequences and Lucas numbers are named after him.
Biography
Lucas was born in
Lucas served as an artillery officer in the French Army during the Franco-Prussian War of 1870–1871.[1]
In 1875, Lucas posed a challenge to prove that the only solution of the Diophantine equation
with N > 1 is when N = 24 and M = 70. This is known as the cannonball problem, since it can be visualized as the problem of taking a square arrangement of cannonballs on the ground and building a square pyramid out of them. It was not until 1918 that a proof (using elliptic functions) was found for this remarkable fact, which has relevance to the bosonic string theory in 26 dimensions.[2] More recently, elementary proofs have been published.[3][4]
He devised methods for testing the
He worked on the development of the umbral calculus.
Lucas is credited as the first to publish the so-called "Smarandache" function.[6]
Lucas was also interested in
Lucas died in unusual circumstances. At the banquet of the annual congress of the Association française pour l'avancement des sciences, a waiter dropped some
Works
- Recherches Sur Plusieurs Ouvrages De Léonard De Pise Et Sur Diverses Questions D’Arithmétique Supérieure (1877)
- Récréations scientifiques (1880)
- Théorie des nombres, Tome Premier (1891)
- Récréations mathématiques (1894)
- L'arithmétique amusante (1895)
See also
References
- ^ a b c O'Connor, John. "Édouard Lucas". MacTutor History of Mathematics archive, University of St Andrews.
- ^ "week95". Math.ucr.edu. 1996-11-26. Retrieved 2012-01-04.
- ^ Ma, D. G. (1985). "An Elementary Proof of the Solutions to the Diophantine Equation ". Sichuan Daxue Xuebao. 4: 107–116.
- JSTOR 2323911.
- ^ "Prime Curios!: 17014...05727 (39-digits)". Primes.utm.edu. Retrieved 2012-01-04.
- ^ Sondow, Jonathan; Weisstein, Eric W. "Smarandache Function". MathWorld—A Wolfram Web Resource.
- ^ Lucas, Édouard (1880). "Récréations scientifiques sur l'arithmétique et sur la géométrie de situation". La Revue scientifique de la France et de l'étranger: Revue des cours scientifiques (in French). 10 (1). G. Baillière: 36–42. Retrieved 2019-05-13.
- Weisstein, Eric W. "Cannonball Problem". MathWorld.
- Williams, Hugh C. (1998). Édouard Lucas and primality testing. Canadian Mathematical Society series of monographs and advanced texts. Vol. 22. New York: ISBN 0-471-14852-0..
- Harkin, D. “On the Mathematical Works of Francois-Édouard-Anatole Lucas, Enseignement mathematique, 2nd ser., 3 (1957), 276–288.