Show that there is an equilateral triangle with angles $\pi/m$ for any integer $m\ge4$. What is the corresponding result for regular n gon? My attempt: I know that area of triangle in hyperbolic plane is $\pi-(sum \ of \ angles\ of\ triangles)$ . Let y axis be my first line choose second line to be a semicircle with centre right of origin such that it makes an angle $\pi/m$ with y axis .Choose third line to be semicircle with centre on left of origin with angle $\pi/m$ with y axis and the area of triangle by the three lines is $3\pi/m$.
1.Why should the third line intersect second line? 2.How do i write this proof rigourously? I have very little knowledge in this subject so i would prefer an elementary answer.