7 Dec
2006
7 Dec
'06
11:53 p.m.
The following 4-parameter expression generates a planar chart of 4 concyclic vertices for any choice of integer parameters a,b,c,d, excepting just one odd; furthermore it generates precisely _all_ those for which two (or three) pairs of opposite edges are equal, modulo permutations of the vertices A,B,C,D: [AB, BC, CA, BD, AD, CD] = [a*b, (a*c+b*d)/2, (a*c-b*d)/2, (a*c-b*d)/2, (a*c+b*d)/2, c*d] I don't know whether a 5-parameter rational parameterisation exists for all concyclic charts. Fred Lunnon