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Note oN ANGEL’Ss METHOD oF INSCRIBING REGULAR POLYGONS. 
By Rospert JupDsoN ALEY. 
On page 47, “Practical Plane and Solid Geometry,” by Henry Angel, 
the following method of inscribing a regular polygon in a circle is given: 
“Let ACB be the given circle, and let the required figure be a hep- 
tagon. Draw the diameter AB, and divide it into seven equal parts. (The 
number of parts is regulated by the required number of sides.) With A 
and B as centers—radius AB—describe two arcs intersecting in D. From 
D draw the line D 2, passing through the second division of the diameter, 
and produce it, to meet the circle in E. The distance, AE, will divide the 
circle into seven equal parts; and if the points of division be joined, a hep- 
tagon will be inscribed in the circle.” 
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The method has the merit of seeming to succeed. When applied to 
circles of short radii, no noticeable error is found in the drawing. I have 
not attempted to give a geometric demonstration of the error which arises 
in this and all similar rule of thumb methods of inscribing regular poly- 
gons. Let the diameter AB, for convenience, be fourteen units in length; 
then, by obvious trigonometric processes, we find AE to be 6.09212 units 
in length, while in a true heptagon the side would be 6.07436 units long. 
