Raoul Bricard
Encyclopedia
Raoul Bricard is a French
engineer
and a mathematician
. He is best known for his work in work in geometry
, especially descriptive geometry
and scissors congruence, and kinematics
, especially mechanical linkages.
in Paris
. In 1932 he received Poncelet Prize
in mathematics
from the Paris Academy of Sciences
for his work in geometry.
, even before the problem was stated by Hilbert
. In it he proved that mirror symmetric
polytope
s are scissors congruent, and proved a weak version of Dehn
's criterion.
In 1897 Bricard published an important investigation on flexible polyhedra. In it he classified all flexible 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 1922.
. He is listed in Encyclopedia of Esperanto
.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
engineer
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...
and a mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is best known for his work in work in geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, especially descriptive geometry
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 in art...
and scissors congruence, and kinematics
Kinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
, especially mechanical linkages.
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 CraftsConservatoire National des Arts et Métiers
The Conservatoire National des Arts et Métiers , or National Conservatory of Arts and Crafts, is a doctoral degree-granting higher education establishment operated by the French government, dedicated to providing education and conducting research for the promotion of science and industry...
in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
. In 1932 he received Poncelet Prize
Poncelet Prize
The Poncelet Prize 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 , mostly for the work in applied mathematics...
in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
from the Paris Academy of Sciences
French Academy of Sciences
The French Academy of 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...
for his work in geometry.
Work
In 1896 Bricard published a paper on Hilbert's third problemHilbert's third problem
The third on Hilbert's list of mathematical problems, presented in 1900, is the easiest one. 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 many polyhedral pieces which can be reassembled to yield the...
, even before the problem was stated by Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
. In it he proved that mirror symmetric
Reflection symmetry
Reflection symmetry, reflectional symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.In 2D there is a line of symmetry, in 3D a...
polytope
Polytope
In elementary geometry, a polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on in higher dimensions...
s are scissors congruent, and proved a weak version of Dehn
Max Dehn
Max Dehn was a German American mathematician and a student of David Hilbert. He is most famous for his work in geometry, topology and geometric group theory...
's criterion.
In 1897 Bricard published an important investigation on flexible polyhedra. In it he classified all flexible octahedra
Octahedron
In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....
. This work was the subject of Henri Lebesgue's
Henri Lebesgue
Henri Léon Lebesgue was a French mathematician most famous for his theory of integration, which was a generalization of the seventeenth century concept of integration—summing the area between an axis and the curve of a function defined for that axis...
lectures in 1938. Later Bricard discovered notable 6-bar linkages.
Bricard also gave one of the first geometric proofs of Morley's trisector theorem
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 Morley triangle. The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley...
in 1922.
Books
Bricard authored six books, including a mathematics survey in EsperantoEsperanto
is the most widely spoken constructed international auxiliary language. Its name derives from Doktoro Esperanto , the pseudonym under which L. L. Zamenhof published the first book detailing Esperanto, the Unua Libro, in 1887...
. He is listed in Encyclopedia of Esperanto
Encyclopedia of Esperanto
Encyclopedia of Esperanto may refer to three different attempts of creating an encyclopedia of all Esperanto topics...
.
- 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