Senior Math Major Honors Defense
Projective Collinearities in Perspective Art by Julie Heymann
Wednesday, April 25, 2012
Abstract. In this paper, we show that any projective collineation is equivalent to the composition of four perspective collineations. In addition, we give our equivalence an interpretation from perspective art. A projective collineation is a bijection from one projective space (whose elements are points and lines) back to itself that preserves incidence. A perspective collineation is a function that sends points to points, that are centered around another point, and lines to lines that are centered around another line. Our proof uses Desargues’ Theorem and the Fundamental Theorem of Projective Geometry to construct a series of projective collineations.
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