The configuration space of triangles up to similarity is naturally a 30-60-90 triangle itself, with its short leg and its hypotenuse forming the locus of all the isosceles (and the vertex between them representing the equilateral). So the "most scalene" would naturally be as far away as possible from that equilateral vertex, along the angle bisector of the two sides respresenting isosceles. That would put it on the line of degenerate triangles having angles (p*pi, (1-p)*pi, 0), to be exact at the one with angles (2*pi/3, pi/3, 0). Since this isn't so interesting, what if we exclude obtuse triangles? In that case the scalenest non-obtuse triangle turns out to be the 30-60-90 one. --Dan Stanley Rabinowitz asked: << Of all triangles, which one is the most scalene (whatever that means)? Sometimes the brain has a mind of its own.