Raoul Bricard (23 March 1870 – 26 November 1943) was a French

engineer Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the l ...

and a

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, structure, space, models, and change. History On ...

. He is best known for his work in

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, especially

descriptive geometry Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and ...

and

scissors congruence The third of Hilbert's list of mathematical problems, presented in 1900, was the first to be solved. The problem is related to the following question: given any two polyhedra of equal volume, is it always possible to cut the first into finitely m ...

, and

kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause ...

, especially

mechanical linkage A mechanical linkage is an assembly of systems connected to manage forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are modeled as providing i ...

Biography

Bricard taught geometry at Ecole Centrale des Arts et Manufactures. In 1908 he became a professor of applied geometry at the National Conservatory of Arts and Crafts 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. S ...

. In 1932 he received the

Poncelet Prize The Poncelet Prize (french: Prix Poncelet) is awarded by the French Academy of Sciences. The prize was established in 1868 by the widow of General Jean-Victor Poncelet for the advancement of the sciences. It was in the amount of 2,000 francs (as of ...

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

from the

Paris Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at th ...

for his work in geometry.

Work

In 1896 Bricard published a paper on

Hilbert's third problem The third of Hilbert's list of mathematical problems, presented in 1900, was the first to be solved. The problem is related to the following question: given any two polyhedra of equal volume, is it always possible to cut the first into finitely m ...

, even before the problem was stated by

Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...

. In it he proved that mirror symmetric

polytope In elementary geometry, a polytope is a geometric object with flat sides (''faces''). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions as an -d ...

s are scissors congruent, and proved a weak version of Dehn's criterion. Br1-anim

In 1897 Bricard published an important investigation on

flexible polyhedra In geometry, a flexible polyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes of all of its faces unchanged. The Cauchy rigidity theorem shows that in dimension 3 such ...

. In it he classified all flexible

octahedra In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...

, now known as Bricard octahedra. This work was the subject of Henri Lebesgue's lectures in 1938. Later Bricard discovered notable 6-bar linkages. Bricard also gave one of the first geometric proofs of

Morley's trisector theorem In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle. The theorem ...

in 1922.

Books

Bricard authored six books, including a mathematics survey in

Esperanto Esperanto ( or ) is the world's most widely spoken constructed international auxiliary language. Created by the Warsaw-based ophthalmologist L. L. Zamenhof in 1887, it was intended to be a universal second language for international communi ...

. He is listed in '' Encyclopedia of Esperanto''. * ''Matematika terminaro kaj krestomatio'' (in Esperanto), Hachette, Paris, 1905
''Géométrie descriptive''
O. Doin et fils, 1911
''Cinématique et mécanismes''
A. Colin, 1921 * ''Petit traité de perspective'', Vuibert, 1924
''Leçons de cinématique''
Gauthier-Villars et cie., 1926
''Le calcul vectoriel''
A. Colin, 1929

Notes

References

* Laurent R., ''Raoul Bricard, Professeur de Géométrie appliquée aux arts'', in Fontanon C., Grelon A. (éds.), ''Les professeurs du Conservatoire national des arts et métiers, dictionnaire biographique, 1794-1955'', INRP-CNAM, Paris 1994, vol. 1, pp. 286–291.

External links

* {{DEFAULTSORT:Bricard, Raoul 19th-century French mathematicians 20th-century French mathematicians 20th-century French engineers Geometers 1870 births 1943 deaths