Project Euler Forum

It seems to me that using the term "torus" in Problem 780 (View Problem) is somewhat misleading. If you actually bound the rectangle to a torus (by first bending it into a calendar, and then connecting the two ends) , the triangles, angles and sides would all be distorted. The problem is really an infinite grid of repeating, duplicate rectangle layouts (which seems consistent with the problem description).
Or am I missing some different transformation of the rectangles onto the torus? I'm only asking in case my interpretation is leading me to an incorrect solution approach.

pismobiker wrote: Sat Oct 12, 2024 3:35 pm Or am I missing some different transformation of the rectangles onto the torus?

Thank you for your query. I'm happy to confirm that your interpretation is perfectly correct.
The plane "quotiented" by a lattice (i.e. the lattice's fundamental parallelogram with opposite edges identified), as described in the problem text, is one standard presentation of the torus; see for example https://mathworld.wolfram.com/Torus.html or https://en.wikipedia.org/wiki/Torus#Topology.

Thank you. Since I'm currently stuck, I was hoping you'd tell how my interpretation was a dumb sophomore mistake -- and that the correct interpretation would get me past my current road block. Think that that only happens in the murder mystery books..... .