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Topic: A Theorem concerning the Trisectors of a Triangle
Replies: 24   Last Post: Nov 10, 1998 12:19 AM

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Russell Towle

Posts: 70
Registered: 12/3/04
Re: A Theorem concerning the Trisectors of a Triangle
Posted: Sep 17, 1998 12:04 PM
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John Conway wrote,

> An interesting question is how many other equilateral triangle
>theorems like Morley's and Napoleon's there are? Erect triangles
>on the edges of ABC with base angles alpha at A, beta at B, gamma
>at C. Then the apices of these form an equilateral triangle if the triple
>alpha,beta,gamma is pi/6,pi/6,pi/6 (Napoleon) or -A/3,-B/3,-C/3
>(Morley). This also happens for -pi/6,-pi/6,-pi/6 and for various
>triples -A'/3,-B'/3,-C'/3 with A',B',C' congruent to A,B,C modulo pi.


John, what intrigues me about this, is, do such patterns operate in higher
spaces? Do we see such behavior in tetrahedra, for instance, with a regular
Platonic tetrahedron arising from the trisection or quadrisection of a
solid angle?

Russell Towle
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Date Subject Author
9/12/98
Read A Theorem concerning the Trisectors of a Triangle
Den Roussel
9/12/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/13/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Larry Cusick
10/27/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/13/98
Read Re: A Theorem concerning the Trisectors of a Triangle
steve sigur
9/14/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Richard Guy
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Richard Guy
9/15/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Richard Guy
9/16/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Floor van Lamoen
9/16/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Floor van Lamoen
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Floor van Lamoen
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Russell Towle
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Russell Towle
9/17/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Douglas J. Zare
9/19/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Russell Towle
9/20/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/20/98
Read Re: A Theorem concerning the Trisectors of a Triangle
John Conway
9/18/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Antreas P. Hatzipolakis
11/10/98
Read Re: A Theorem concerning the Trisectors of a Triangle
Den Roussel

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