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/

IMaGe LINKS

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.

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

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:

In Solstice: An Electronic Journal of Geography and Mathematics:

- Volume XVIII, Number 2, 2007 (all by Sandra Lach Arlinghaus)
**Special Issue on Projective Geometry Constructions**- Geometry/Geography,
Visual Unity

- The
Animated Pascal

- Desargues's Two-Triangle Theorem
- Volume XVII, Number 1, 2006 Zipf's Hyperboloid? Sandra L. Arlinghaus and Michael Batty

Software
used in analysis:

- DevInfo
5.0: http://www.devinfo.org/

- Adobe
^{®}PhotoShop and ImageReady - Adobe
^{®}DreamWeaver - ESRI:
- ArcView
^{®}3.2 - ArcGIS
^{®}9.2 - ArcCatalog
^{®} - ArcMap
^{®} - Google
Earth
^{®}

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/

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.