Cardioids and Morley’s trisector theorem

Abstract

Since the beginning of the twentieth century, many other proofs of Morley’s theorem have been published. An article in the November 1978 issue of The American Mathematical Monthly by Cletus Oakley and Justine C. Baker (with supplements by Charles W. Trigg), see [3], lists no less than 150 references. Some only give a proof of the simple version of the theorem. But many proofs not only consider inner trisectors, but also their outer counterparts. In fact, if all trisectors are extended to full lines, there are precisely eighteen trisectors: six for each vertex of ABC, the outer ones making angles of /3 !r with the inner trisectors through the same vertex. Note that the directed angle from one line to another is determined modulo r, so trisectors are determined modulo /3 r . From these eighteen trisectors many more equilateral Morley triangles can be constructed, as will be indicated in the next section. Since 1978, numerous other articles and notes on Morley’s theorem have appeared in print.

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Cite this paper

@inproceedings{Oakley2017CardioidsAM, title={Cardioids and Morley’s trisector theorem}, author={C. Elizabeth Oakley}, year={2017} }