Right Angles in a Triangle

Date: 3/8/96 at 13:36:1
From: Anonymous
Subject: right angles

How many right angles (90 degrees) can a triangle have?

Date: 3/17/96 at 19:42:53
From: Doctor Jodi
Subject: right angles

That depends where the triangle is... 

If it's on a plane (like a table top), only one.

If it's on a sphere, it could have more than one.  Can you picture 
this?

The straight lines in a plane - the shortest distance between any two 
points - are analogous to great circles on a sphere.

The general word for the shortest path between two points in any 
surface is a <b>geodesic</b>.  Straight lines in the plane and great 
circles on the sphere are both sorts of geodesics.

What, you may ask, does a great circle look like?

Well, suppose you take a play-dough sphere and cut it into two equal 
parts (two semi-spheres).  The line you cut on is a <b>great circle</b>.

There are infinitely many great circles on the sphere; you could 
make infinitely many semi-spheres, if you felt like it.  

Now, if instead of cutting your play-dough sphere, you just MARK 
several great circles on it, you can make a triangle.  (Triangles on 
any surface are made with geodesics, so on a sphere, you need to use 
great circles).

How many perpendicular great circles can you use in one triangle? 
That's how many right angles it will have...

Good luck!

-Doctor Jodi,  The Math Forum