Two twisty doughnut shapes solve a 150-year-old geometry puzzle

Compact Bonnet pairs: isometric tori with the same curvatures (Bobenko, A.I., Hoffmann, T. & Sageman-Furnas, A.O. Compact Bonnet pairs: isometric tori with the same curvatures. Publ.math.IHES 142, 241–293 (2025). https://doi.org/10.1007/s10240-025-00159-z)

In 1867, French mathematician Pierre Ossian Bonnet proved something that seemed like common sense: …