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/
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