Date: 08/30/98 at 07:52:58 From: Paul Baker Subject: Geometric construction of an arc Dear Dr. Math, In an earlier geometry class I had, we learned how to take a triangle (specificaly the 2d representation of a cone) and, using a compass, draw what the cone would look like "rolled out." All I can remember is that it had something to do with chord lengths or their relations. My teacher didn't know, and my school recently changed textbooks, and the new ones for that class no longer include that construction. Thank you for your time. Sincerely, Paul Baker
Date: 08/31/98 at 12:16:35 From: Doctor Peterson Subject: Re: Geometric construction of an arc Hi, Paul. As I understand your question, you want to know how to draw a shape that you could cut out and roll up to form a cone whose cross-section you are given. * - * - ** - * - * - * +- * |A * /\ | * / \ | * / \ | * / \L L| ** / \ | * pi * D / \ | ** / \ | *** / D \ | ***** -------------- ****** The shape you want to draw will be a sector of a circle with radius equal to the slant height (L) of the cone, and arc length equal to the circumference (pi * D) of the base. The angle A then will be: pi * D 180 * D ------ * 180 degrees = ------- degrees pi * L L If you are looking for a compass-and-straightedge construction of this angle, my first impression is that it may be impossible. Let me know if this is not what you wanted. - Doctor Peterson, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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