Projective Geometry - Course Description
Wednesday, August 15, 2012
"“An approach to the secrets of space from the standpoint of artistic and imaginative insights.” - Lawrence Edwards
The 11th Grade Projective Geometry block is a challenging, highly imaginative, synthetic approach to geometry, stretching the limits of our traditional “Euclidean” worldview. Through various geometric constructions first discovered by Pappus, Desargues, Pascal, and Brianchon, students explore the ways in which mathematicians for 2000 years flirted with the ideas which we now recognize as projective constructions. The effort moved forward when artists in the 15th century began to wonder how to depict scenes on flat paper which appeared to be three dimensional. Projective Geometry was only recognized and developed as late as the 19th century. Through these explorations, we will come to appreciate a completely unfamiliar space and reality which is just as valid, and in fact more generally true, than the one with which we are more used to dealing. We will especially explore the concept of infinity, that is, an infinite and yet closed Projective space. Euclidean geometry can then be understood as a special case of Projective geometry, in which certain points have been fixed ""at infinity"" and only after this is done can such concepts as inside/outside, measurement, congruence and angle gain meaning. Working with this fascinating geometry will naturally lead to more philosophical questions about the senses that we humans tend to prioritize (touch) over others (sight), and how our own consciousness is constantly (usually unnoticed by us) striving to synthesize these senses into a coherent world picture.
Faculty: Brian Gleichauf, High School Sciences Teacher
Class Dates: April 29th-May 17th, 2013
Curriculum Area: Morning Lesson Block
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