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Isoperimetric 2mn-gons applied to finding concisely by a new construction

Published online by Cambridge University Press:  20 January 2009

R. E. Anderson
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1. Let AB be the half-side of any n-gon, OB its in-radius (r), and OA its circum-radius (R). Draw OA11 to bisect ∠ AOB and AA1C ⊥ to it meeting OB in C. Then A1B2 to AB is the half-side of a 2n-gon having the same perimeter as the n-gon, OB1 its inradius (r1), and OA1 its circum-radius (R1).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , February 1894 , pp. 150 - 152
Copyright
Copyright © Edinburgh Mathematical Society 1894