A Triangle with Three Right Angles

Date: 12/01/1999 at 08:48:06
From: Jimmy Stine
Subject: Geometry

For extra credit my teacher assigned this problem: How could you make 
a triangle with three right angles? I have tried for a while to do it 
and I have to somehow make a model of a triangle with 3 right angles. 
Could you please send me the solution? 

Date: 12/01/1999 at 12:13:27
From: Doctor Peterson
Subject: Re: Geometry

Hi, Jimmy.

This is impossible for a real triangle on a plane, since, as you 
probably know, the sum of angles must be 180 degrees. But it is 
possible in spherical geometry, where we use the word "line" to mean a 
great circle (a circle around the sphere whose plane goes through the 
center of the earth). 

Imagine starting, say, at the North Pole, walking some distance in a 
"straight line," turning left 90 degrees, walking some distance, then 
turning left 90 degrees again, and getting back where you started. Can 
you find a way to do this, and end up 90 degrees from your original 
direction?

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/