# Émile Léger

### Quick Info

Lagrange-aux-Bois, France

Paris, France

**Émile Léger**was a French mathematician who was the first to notice that the Euclidean algorithm converges most slowly for consecutive Fibonacci numbers.

### Biography

**Émile Léger**'s father was Claude Léger who was a professor of rhetoric at the Lycée de Mayence (the city of Mainz, now in Germany, which was occupied by the French at that time). Émile Léger was admitted to the École Polytechnique in 1813.

He was still a student at the École Polytechnique in March 1815 when Napoleon Bonaparte escaped for his Hundred Days. The students were told to defend Paris and Léger was decorated for his bravery defending the capital.

In 1816 he left the École Polytechnique and joined his family in Montmorency where he father had set up his own educational establishment. He taught at his father's school taking charge after his father retired. The school was very successful in training students for the entrance examinations for university, in particular training students to enter the École Polytechnique.

Léger only published four mathematical papers but one contains possibly the first mention of what today is a well known fact about the Euclidean algorithm, see [1]:-

Émile Léger appears to have been the first (or second, if the work of de Lagny ... is counted) to recognise that the worst case of the Euclidean algorithm occurs when the inputs are consecutive Fibonacci numbers.

### References (show)

- J Shallit, Analysis of the Euclidean Algorithm,
*Historia Mathematica***21**(1994), 401-419.

Written by J J O'Connor and E F Robertson

Last Update December 1997

Last Update December 1997