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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 45^{0}. 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 java applet was produced using JavaSketchpad. The following
is the maker's beta on this product:

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).

Arthur's Home Page

This page was created November 30th, 1998.

URL: http://www.nevada.edu/~baragar/geom/sevteen.htm