Recent Examples on the WebIn other words, the sum of all the local curvatures of a three-dimensional shape is the same for all topologically equivalent shapes with the same surface area. Spyridon Michalakis, Scientific American, 1 Aug. 2020 Two shapes are topologically equivalent if one can be transformed into the other without any cutting or gluing.Quanta Magazine, 12 May 2020 Thus, a coffee cup and a doughnut are what’s known as topologically equivalent. Sophia Chen, Wired, 9 Mar. 2020 In two dimensions, any two manifolds with the same Euler characteristic are topologically equivalent.Quanta Magazine, 13 Jan. 2015