Michel ChaslesMichel Floréal Chasles (miʃɛl flɔʁeal ʃal; 15 November 1793 – 18 December 1880) was a French mathematician. He was born at Épernon in France and studied at the École Polytechnique in Paris under Siméon Denis Poisson. In the War of the Sixth Coalition he was drafted to fight in the defence of Paris in 1814. After the war, he gave up on a career as an engineer or stockbroker in order to pursue his mathematical studies.
Lazare CarnotLazare Nicolas Marguerite Carnot (lazaʁ nikɔla maʁɡəʁit kaʁno; 13 May 1753 – 2 August 1823) was a French mathematician, physicist, politician and a leading member of the Committee of Public Safety during the French Revolution. His military reforms, which included the introduction of mass conscription (levée en masse), were instrumental in transforming the French Revolutionary Army into an effective fighting force.
Girard DesarguesGirard Desargues (ʒiʁaʁ dezaʁɡ; 21 February 1591 - September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry. Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon are named in his honour. Born in Lyon, Desargues came from a family devoted to service to the French crown. His father was a royal notary, an investigating commissioner of the Seneschal's court in Lyon (1574), the collector of the tithes on ecclesiastical revenues for the city of Lyon (1583) and for the diocese of Lyon.
Compass (drawing tool)A compass, more accurately known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to mark out distances, in particular, on maps. Compasses can be used for mathematics, drafting, navigation and other purposes. Prior to computerization, compasses and other tools for manual drafting were often packaged as a set with interchangeable parts. By the mid-twentieth century, circle templates supplemented the use of compasses.
Intersection theoremIn projective geometry, an intersection theorem or incidence theorem is a statement concerning an incidence structure – consisting of points, lines, and possibly higher-dimensional objects and their incidences – together with a pair of objects A and B (for instance, a point and a line). The "theorem" states that, whenever a set of objects satisfies the incidences (i.e. can be identified with the objects of the incidence structure in such a way that incidence is preserved), then the objects A and B must also be incident.
Perspective (geometry)Two figures in a plane are perspective from a point O, called the center of perspectivity, if the lines joining corresponding points of the figures all meet at O. Dually, the figures are said to be perspective from a line if the points of intersection of corresponding lines all lie on one line. The proper setting for this concept is in projective geometry where there will be no special cases due to parallel lines since all lines meet. Although stated here for figures in a plane, the concept is easily extended to higher dimensions.
Circular points at infinityIn projective geometry, the circular points at infinity (also called cyclic points or isotropic points) are two special points at infinity in the complex projective plane that are contained in the complexification of every real circle. A point of the complex projective plane may be described in terms of homogeneous coordinates, being a triple of complex numbers (x : y : z), where two triples describe the same point of the plane when the coordinates of one triple are the same as those of the other aside from being multiplied by the same nonzero factor.
