|
Sub-proof 1: An isoseles triangle maximizes the volume to perimeter ratio.
Let x, y and z be the sides of the triangle, with x equal y for an isoseles.
Perimeter P1= x+y+z
since x=y
P1=2x+z
Area A1=1/4zx + 1/4 zy
since x=y
A1=1/2zx
Therefore (I don't know the ASCII code for the three dots)
A1/P1 = (1/2zx) / (2x+z)
= zx / 2(2x+z)
= zx / (4x+2z)
OK, I'm thinking this might not be the right direction to go since I must now calculate the differences in the perimiter based on movement around the circle.
|