Projective Geometry Leads to the Unification of All Geometries
Overview
The nineteenth century witnessed a great change in the nature of geometry. From beginnings in perspective drawing of artists in the eighteenth century, mathematicians developed projective geometry, and with the work of Jean-Victor Poncelet geometry became the study of properties of figures that remain unchanged under families of transformations. These transformations now became the objects of study, and different geometries would eventually be seen as parts of one unified whole.
Background
Since ancient times, geometry has always been at the heart of mathematics; mathematicians in ancient Greece were referred to as "geometers." During the Renaissance, when Europe had recovered from the Black Death (bubonic plague), dynastic rule became the standard form of government, and economies were again growing, there was a renewed interest in the classical works of the ancient Greeks. Thus, geometry returned to take its place in the curriculum of the newly established European universities. Classical works in geometry from Euclid, Archimedes, Apollonius, and Pappus were returned to Europe via Byzantium and the Arab states, and these works were restored, translated, and studied. This set the stage for the later development of new branches of geometry.
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