TAXICAB GEOMETRY

by

Susan Sexton

 

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Foundations of Geometry I Project

University of Georgia

Fall 2006

Instructor: Clint McCrory

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A little bit of history . . .

Most who have studied geometry at some point in school have studied Euclidean geometry.

This type of geometry dates back over 2000 years ago.

It has influenced much of how geometry is taught today.

 

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Euclid

 

to learn more about Euclid and his works visit:

http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Euclid.html

or

http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

 

 

Taxicab geometry is a non-Euclidean geometry.

It is similar to Euclidean geometry in many aspects.

However, there are fundamental differences between the two geometries.

 

 

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Some more history . . .

Hermann Minkowski, a German mathematician and a teacher of Albert Einstein,

is credited as the first to propose taxicab geometry.

He did so by proposing that the notion of distance in Euclidean geometry

is different than the notion of distance in taxicab geometry.

In fact, he proposed a family of metrics where the notion of distance

is different depending on the space in question.

 

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Hermann Minkowski

to learn more about Minkowski and his works visit:

http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Minkowski.html

or

http://en.wikipedia.org/wiki/Hermann_Minkowski

 

 

 

 

In 1952 Austrian mathematician Karl Menger established an exhibit at the Museum of Science and Industry of Chicago.

At this exhibit he distributed a booklet entitled You Will Like Geometry.

It is in this booklet that the term taxicab is first used.

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Karl Menger

to learn more about Menger and his works visit:

http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Menger.html

or

http://en.wikipedia.org/wiki/Karl_Menger

 

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