Of all triangles, which one is the most scalene (whatever that means)?
The least scalene triangle is the equilateral triangle, which has the largest area for its size, so the most scalene triangle is probably a degenerate triangle with zero area. From a standard deviation perspective, the limit is side lengths (0, 1, 1), but that's essentially isosceles. Another perspective on unequal sides is to maximize the differences between the side lengths. Treating (maximum - middle) and (middle - minimum) as two sides of a rectangle, the limits of the sides that maximize the area of the rectangle are in the proportions of (1, 3, 4), but that's also degenerate. Balancing the desire for the triangle to have maximal area and for the side lengths to be maximally unequal (in the rectangular area sense, above), I get side lengths in the proportion of (0.284634809, 0.754329904, 1), or approximately (263, 697, 924). Kerry -- lkmitch@gmail.com www.kerrymitchellart.com