Projective Geometry in the seventeenth century
To paint the world as they see it, painters developed a system of focused perspective inspiring new geometrical ideas. Euclidean geometry is tactile because it agrees with the sense of touch but not always with the sense of sight, it deals with lines that never meet but we never see parallel lines. The artist draws parallel lines that converge, introducing foreshortening and perspective to give the eye an illusion of reality.
This motivated mathematicians to search for theorems on the intersection of lines and curves.
Girad Desargues (1596-1662) was the first major mathematician to explore the suggestions arising out of the work on perspective.
Pascal (1623-1662) proved a theorem in projective geometry at the age of 16.
Projective Geometry in the nineteenth century
Brianchon (1783-1864) worked during the early nineteenth century revival of projective geometry. He created a theorem that states that:
If a hexagon is circumscribed about a circle the lines joining opposite vertices meet in one point, this theorem applies to any conic section.
To make a map we have to project figures from a sphere into a flat sheet. The principles involved are the same as those of perspective and projective geometry.
Gerard Mercator (1512-94) the Flemish cartographer developed the most famous method, the Mercartor's projection.
New Geometry, New Worlds
Golden Age of Greek Geometry
History of Mathematics Module
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