__NOTOC__ François Édouard Anatole Lucas (; 4 April 1842 – 3 October 1891) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. 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

Amiens Amiens (English: or ; ; pcd, Anmien, or ) is a city and commune in northern France, located north of Paris and south-west of Lille. It is the capital of the Somme department in the region of Hauts-de-France. In 2021, the population of ...

and educated at the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education Secondary education or post-primary education covers two phases on the International Standard Classification of Education sca ...

. He worked in the Paris Observatory and later became a professor of mathematics at the Lycée Saint Louis and the Lycée Charlemagne in

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. ...

. Lucas served as an artillery officer in the French Army during the Franco-Prussian War of 1870–1871. In 1875, Lucas posed a challenge to prove that the only solution of the Diophantine equation: :

\sum_^ n^2 = M^2\;

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. More recently,

elementary proof In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. Historically, it was once thought that certa ...

s have been published. He devised methods for testing the primality of numbers. In 1857, at age 15, Lucas began testing the primality of 2¹²⁷ − 1 by hand, using Lucas sequences. In 1876, after 19 years of testing, he finally proved that 2¹²⁷ − 1 was prime; this would remain the largest known

Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17 ...

for three-quarters of a century. This may stand forever as the largest prime number proven by hand. Later Derrick Henry Lehmer refined Lucas's primality tests and obtained the Lucas–Lehmer primality test. He worked on the development of the

umbral calculus In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain "shadowy" techniques used to "prove" them. These techniques were introduced by John Bliss ...

. Lucas was also interested in recreational mathematics. He found an elegant binary solution to the Baguenaudier puzzle. He also invented the Tower of Hanoi puzzle in 1883, which he marketed under the nickname ''N. Claus de Siam'', an anagram of ''Lucas d'Amiens'', and published for the first time a description of the Dots and Boxes game in 1889. 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 crockery and a piece of broken plate cut Lucas on the cheek. He died a few days later of a severe skin inflammation probably caused by

sepsis Sepsis, formerly known as septicemia (septicaemia in British English) or blood poisoning, is a life-threatening condition that arises when the body's response to infection causes injury to its own tissues and organs. This initial stage is foll ...

. He was only 49 years old.

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)

References

* *. *Harkin, D. “On the Mathematical Works of Francois-Édouard-Anatole Lucas, ''Enseignement mathematique'', 2nd ser., 3 (1957), 276–288.

External links

*
Scans of Lucas's original Tower of Hanoi puzzle in French, with translations
by Clark Kimberling
Édouard Lucas
{{DEFAULTSORT:Lucas, Edouard 1842 births 1891 deaths 19th-century French mathematicians Number theorists École Normale Supérieure alumni Fibonacci numbers Recreational mathematicians Mathematics popularizers Deaths from sepsis People from Amiens

Biography

Works

See also

References

External links