*TAXICAB GEOMETRY*

by

Susan Sexton

Foundations of
Geometry I Project

University of
Georgia

Fall 2006

Instructor: Clint
McCrory

* *

*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.

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.

* *

* *

*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.

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 ÒtaxicabÓ is first used.

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