Find the hyperbolic area of the euclidean rectangle with vertices (0,1) , (0,3),(5,3),(5,1).
the area of a hyperbolic triangle is equal to its Defect. Now any hyperbolic polygon can be divided into hyperbolic triangles to get the area. But with this euclidean rectangle two sides are not geodesics. Will an inversion work? Is there another method to find the Hyperbolic area of a euclidean figure?
Thank You.
I'm still trying to figure this out. Drawing the diagonal doesn't work because of the reason i mentioned above. All lines of the hyperbolic triangle must be geodesics. A possible route to the solution is using integrals (double at that). I'm horrible with those. Going to review all of calculus this summer then definitely i will be a great helper on this forum......But i need help now .