The regular seventeen-gon

The following is a construction of the regular seventeen-gon, due to Richmond (1893).
Start with the circle centered at A and going through P(0).  Let the perpendicular at A intersect the circle at B.  Let C be placed such that AC is one quarter of AB.  Let CD quadrisect the angle P(0)CA.  Let E be the point on the line AP(0) such that the angle ECD is 450.  Construct the circle with diameter EP(0), and let it intersect AB at F.  Construct the circle centered at D and through F.  Let this circle intersect AP(0) at G and H.  The perpendiculars at G and H intersect the original circle at P(3), P(5), P(12) and P(14).  Construct the circle centered at P(3) and through P(5).  This intersects the original circle again at P(1), and using P(0) and P(1), we can find all the vertices of the regular seventeen-gon.

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This is a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright ©1990-1998 by Key Curriculum Press, Inc. All rights reserved. Portions of this work were funded by the National Science Foundation (awards DMI 9561674 & 9623018).

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This page was created November 30th, 1998.
URL:  http://www.nevada.edu/~baragar/geom/sevteen.htm