I wonder whether presented in wikipedia square (with angles $120^{\circ}$) is the biggest (taking into account lengths of sides) possible square on a sphere?
- If not what is the biggest?
- If so how it can be proved?
One can assume here definition of a square on a sphere:
Square on a sphere = the 4-sided polygon with equal length sides and equal angles, sides are determined by 4 different great circles.