This question is a continuation of my previously posted question: Was Gauss aware of the non-euclidean implications of his work on moduler forms?, and is based on the information given in John Stillwell's book "Mathematics and it's history", where it's mentioned that using his theory of modular forms Gauss discovered a tessellation of the unit disk by "equilateral triangles" (but curved) of angles: $\pi/4,\pi/4,\pi/4$.
My previous question was about how Gauss interpreted his own computations with modular forms. In this question i don't wish to know if Gauss was aware of the Poincare disk model of hyperbolic geometry, but it's more about placing his calculations in the right context.
From looking in his writings i gained the impression that he was quite aware of the action of the modular group in the upper-half plane (although he didn't view it as a model of the hyperbolic plane) - his nachlass contains drawings of the fundamental domain of the modular group, and he, for example, proved a remarkable result on the mutual connection of all values of the arithmetic-geometric mean of two complex numbers (see David Cox's paper: "AGM of Gauss").
But i didn't find things that look like computations of tessellations of the unit disk (by curved triangle). In his commentary on p. 99-102 of the 8th volume of Gauss's werke ("Three Fragments About Elliptic Modulfunctions"), Fricke gives some related sources (such as one of Gauss's articles on the orbit of pallas, where he is supposed to use some of his analytic work in implicit way), and mentions that the drawing of tessellation of the unit disk was found among his writings. I guess one of the problems is that Google translate doesn't make very good transations.
So my question is:
- Since i'm not sure that p. 99-102 in volume 8 is really the place where he is supposed to make calculations about tessellations, i'm asking for reference - if anyone who is famililar enough with these themes can help, i'll be grateful. If someone sees a formula that resembles a formula he knows from the theory of tessellations of the unit disk in one of Gauss's writings,i'll be glad if he will mention it here.