Computation of not normalized periods of the first and second kinds, and the vector of Riemann  constants will be presented. Finding the vector of Riemann constants on a non-hyperelliptic curve seems to be an open problem, which is now effectively solved.

We compute the associated system of first and second kind periods, which are required for  computation of multiply periodic ℘-functions. The latter are used for uniformization of the curve by  means of the Jacobi inversion problem.

The Pythagorean Theorem is old news. Pythagoras was born in 570 BC but, in fact, we know proofs of “his” theorem that are much, much older than Pythagoras himself. Nowadays there are over 350 different proofs of the Pythagorean theorem in print, and yet many rejoiced when two high-school students from New Orleans, Ne’Kiya Jackson and Calcea Johnson, discovered a new proof of the theorem in 2023. However, is this theorem relevant today? Why is there such an emphasis on this particular theorem? Why would anyone be excited about a new proof of a theorem that already has over 350 proofs? Why are new proofs of old theorems interesting? More importantly, do you know a proof of this theorem?

In this talk we will discuss all of these questions, and present a few proofs along the way, including the recent one by Jackson and Johnson.