Spatial Synthesis
Volume II, Book 2:
Making It Clear:  The Importance of Transparency
Sandra Lach Arlinghaus
sarhaus@umich.edu
http://www-personal.umich.edu/~sarhaus/
ANNOTATED RELATED LINKS
DESARGUES'S TWO TRIANGLE THEOREM


IMaGe LINKS
The links in this section suggest the power of Google Earth in visualizing non-Euclidean geometry theorems.  The image above uses transparency to look through the otherwise complicated appearance of Desargues's Two Triangle theorem from Projective Geometry.  The lines joining corresponding vertices of two triangles are concurrent, forming a tower with these triangles as sections.  In this case, the tower is situated over the Sidney Smith Building of the University of Toronto, home to the Department of Mathematics and the late, great, geometer Professor H. S. M. Coxeter:  mathematics history is linked to the mathematics itself.  Transparency makes the locations of intersection points of corresponding sides, and their associated collinearity, become clear.  Visualizing a two-dimensional theorem in three dimensions, using semi-opaque colors, makes geometric relationships become clear.

In Solstice:  An Electronic Journal of Geography and Mathematics:

TABLE OF CONTENTS
Software used in analysis:
Author affiliation:
Arlinghaus, Sandra Lach.  Adjunct Professor of Mathematical Geography and Population-Environment Dynamics, School of Natural Resources and Environment, The University of Michigan.  Executive Committee Member (Secretary) Community Systems Foundation, sarhaus@umich.edu, http://www-personal.umich.edu/~sarhaus/
Published by:
Institute of Mathematical Geography

http://www.imagenet.org
http://deepblue.lib.umich.edu/handle/2027.42/58219
October, 2008.
 Copyright by Sandra Arlinghaus, all rights reserved.