Projective geometry is an example of mathematics that was originally created with one application in mind, and yet has unexpectedly shed light on fields that are totally unrelated to the one for which it was originally developed. Created by artists during the Renaissance for analyzing perspective, projective geometry blossomed during the eighteenth and nineteenth centuries into a complete revision of the entire field of geometry. Recently it has provided the setting for the modern study of algebraic equations, and has even played a role in physics in the mathematics of quantum field theory.
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