
Re: A Theorem concerning the Trisectors of a Triangle
Posted:
Sep 17, 1998 12:04 PM


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 Giant Gap Press: books on California history, digital topographic maps P.O. Box 141 Dutch Flat, California 95714  Voice: (916) 3892872 email: rustybel@foothill.net 

