Right Angles in a TriangleDate: 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 |
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