Charles Bioche

Charles Marie Paul Bioche (born September 27, 1859 in Paris , † August 19, 1949 in Ferrières-en-Brie ) was a French mathematician and mathematics teacher .

Life

Bioche attended the Collège Stanislas in Paris and studied from 1879 at the École normal supérieure , where he made friends with Henri Bergson . After that he was a school teacher in Mâcon and Poitiers . In 1884 he received his agrégation in mathematics and taught from 1885 at the Lyceum in Douai and from 1889 at the Lycée Michelet in Paris, followed by the Collège Stanislas and from 1897 the Lycée Louis-le-Grand , where he stayed until his retirement in 1925.

He mainly published on geometry. In 1909 he was president of the Société mathématique de France . He was editor of the Revue de l'Ecole and of L'Education mathématique. Since 1909 he was the French section of the International Commission on Mathematical Instruction (ICMI).

Bioche rules

The Bioche rule for variable substitution in integrals of functions that are fractions of real polynomials P, Q in two variables with sine and cosine functions as arguments are named after him . Is to be calculated ${\displaystyle f(t)={\frac {P(\sin t,\cos t)}{Q(\sin t,\cos t)}}}$

${\displaystyle \int f(t)\mathrm {d} t}$,

Then, depending on the behavior, a distinction is made between the following cases: ${\displaystyle \omega (t)=f(t)\mathrm {d} t}$

• ${\displaystyle \omega (-t)=\omega (t)}$: Variable transformation ${\displaystyle u(t)=\cos(t)}$
• ${\displaystyle \omega (\pi -t)=\omega (t)}$: Variable transformation ${\displaystyle u(t)=\sin(t)}$
• ${\displaystyle \omega (\pi +t)=\omega (t)}$ Variable transformation ${\displaystyle u(t)=\tan(t)}$
• if two of the previous conditions apply: variable transformation ${\displaystyle u(t)=\cos(2t)}$
• in all other cases variable transformation . ${\displaystyle u(t)=\tan(t/2)}$

Fonts

• Introduction à l'étude de la géométrie moderne, Paris: C. Delagrave, 1891
• Éléments de géométrie à l'usage des classes de lettres, Saint Cloud: Belin, 1895
• Histoire des mathématiques, Paris: Belin Frères, 1914
• Petit guide pour étudier les mathématiques, Paris: Hatier, 1942

Web links

• Biography at the ICMI