Three-sided Square on a Sphere

Wait a minute, what? A three-sided square? That's not logically possible.

Maybe this was your first thought after you read the title of my project "Three-sided Square on a Sphere". To be honest it may sounds a bit weird first but let me explain the thoughts behind the idea of this project.
Let us start how to define a square. Most people will answer if you are going to ask them how: "Would you define a square?". Maybe answer something about 90-degree angles and all sides have the same length. And they aren't completely wrong! So let's define a square as a shape with only 90-degree angles and all the sides are the same length.

I guess until this point you perfectly agree with me but let's start to go one more step. All this knowledge we already earned at the elementary school as a triangle has at all180-degrees isn't wrong but only correct under the permission of zero curvature. And that's the way how we are able to create a three-sided square. Because the ball has a constant Gau