Question

hyperbolic geometry: using degree measure and k=1, show that a triangle with area 3 can be divided into three triangles each with area 1.

Answer 1

ANSWER :-

Given that ,

k = 1

here we need to prove that

a triangle with area 3 can be divided into three triangles each with area 1.

we already know that the area of a triangle

  

but   

then R = 1 , R = 1 , R = 1.

then 1+1+1 = 3

triangle with area 3 can be divided into three triangles each with area 1.

Note:

Formation of triangle is based on Triangle inequality i.e. sum of the lengths of any two sides of a triangle must be greater than the length of the third side