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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Distance in Taxicab Geometry

 

Taxicab geometry is very similar to Euclidean coordinate geometry.

The points, lines, angles are all the same and measured in the same way.

What is different is the notion of distance.

 

In Euclidean coordinate geometry distance is thought of as “the way the crow flies”.

 

In taxicab geometry distance is thought of as the path a taxicab would take.

 

The blue path from point A to B is the Euclidean distance from A to B.

The red path is the taxicab distance from A to B.

 

While there is only one Euclidean path from A to B, there are multiple taxicab paths from A to B.

 

 

  

These are a few examples of taxicab paths from A to B.

Which is the shortest path?

Can you find an even shorter path?

What do you think would be the path a taxicab driver would take?

 

 

 

The taxicab distance is defined as the sum of the

lengths of the vertical and horizontal distances from A to B.

 

 

Mathematically, the distance formulas for each geometry are:

 

 

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