Until recently, i thought that the first to observe the connection between modular forms and the hyperbolic plane (a model of non-euclidean geometry) was Felix Klein. But in the last week i read the chapter on non-euclidean geometry in the book of John Stillwell - "Mathematics and it's history", where it's mentioned that using his theory of modular forms Gauss discovered a tessellation of the Poincare disk model by equilateral triangles of angles: $$\pi/4,\pi/4,\pi/4$$.

So how Gauss could accomplish this without knowing the hyperbolic plane? i understand that this work was done in the context of elliptic functions and modular forms (not hyperbolic geometry), but the fact that he used triangles with angles sum less than pi, suggests that he might suspect that it's connected with hyperbolic geometry. Also, the fact that Klein studied very closely the writings of Gauss might suggest that this accomplishment has historical influence.

So i'll be glad to clarify this "historical corner".