Descartes' Formula (Geometry and the Imagination)
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Conway, Doyle, Gilman, Thurston; The Geometry Center  
The angle defect at a vertex of a polygon was defined to be the amount by which the sum of the angles at the corners of the faces at that vertex falls short of and the total angle defect of the polyhedron was defined to be what one got when one added up the angle defects at all the vertices of the polyhedron. We call the total defect T. Descartes discovered that there is a connection between the total defect, T, and the Euler Number EVF. Two proofs are given, to be discussed.  


Levels:  Middle School (68), High School (912) 
Languages:  English 
Resource Types:  Lesson Plans and Activities 
Math Topics:  Polyhedra, Triangles and Other Polygons 
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