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Information and research about the geometry invented by Herman Minkowski
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Taxicab Geometry

Angles / Trigonometry

Length / Area / Volume

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The Taxicab Metric

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Kevin's Corner

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I received a Bachelor of Science degree in Mathematics (with a minor in Physics) from Sam Houston State University in 1995 followed by a Master of Science degree in Mathematics from Oregon State University in 1997. My advisor at OSU was Tevian Dray.

I became interested in taxicab geometry in a survey of geometry course taught by Tevian in 1996. Part of this course required a short research paper on taxicab geometry (as I recall) since research in the geometry was so accessible. I chose to research angles and trigonometry in taxicab geometry. When I decided to leave OSU after a MS degree, I extended and polished the taxicab geometry paper I had written and used it as my Master's thesis.

This paper, not published until 2000 in the Pi Mu Epsilon Journal, was one of the early research papers in modern taxicab geometry. As it turned out, Rüstem Kaya in Turkey was doing the same research on angles and trigonometry at the same time I was, although this was not known to me (or him I would imagine) until many years later since communications and knowledge spread much slower in those days. (His paper was published in 1997 about the time I graduated and three years before Tevian and I managed to publish our paper.) This research seemed to be the spark that ignited research in taxicab geometry. The volume of research before 1997 amounted to a handful; since then dozens of papers have been published.

While restarting research in taxicab geometry in 2010, I found there was not a single cohesive website that delved deeply into taxicab geometry. A number of websites had good introductions, and there were scattered pages on deeper topics, but nothing comprehensive. So, I decided to create this website to be as complete a resource on taxicab geometry as I could manage.

Enjoy!

Taxicab geometry papers I have authored:

Taxicab Angles and Trigonometry (Abstract / PDF / HTML -- secondary: PDF / HTML)
- Kevin Thompson and Tevian Dray (1997)
- The Pi Mu Epsilon Journal, Worcester, MA. Vol. 11, No. 2 (Spring 2000), pp. 87-96

Arbitrary Sectioning of Angles in Taxicab Geometry (PDF)
- Kevin P. Thompson (2010)
- Unpublished

The Nature of Length, Area, and Volume in Taxicab Geometry (PDF Mirror)
- Kevin P. Thompson (2010)
- International Electronic Journal of Geometry, Vol. 4, No. 2 (2011), pp. 193-207

Taxicab Triangle Incircles and Circumcircles (PDF)
- Kevin P. Thompson (2010)
- (to appear in The Pi Mu Epsilon Journal)
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