Triangle or Square?

What is the optimum shape for a thinsat?

Triangle

Square

Tri.png

Quad.png

Area

A = \sqrt{3} T^2 / 4

A = Q^2

Side

T = 2 \sqrt{A / \sqrt{3} }

Q = \sqrt{A}

Ratio

T = ( 2 /\sqrt[4]{3} ) Q ~ \approx ~ 1.51967 Q

Q = ( \sqrt[4]{3}/2 ) T ~ \approx ~ 0.65804 T

Rotational
Center

TriA.png

TriB.png

QuadA.png

QuadB.png

Moment
of
Inertia