To answer the question that between a circle and a square, which one is more symmetrical, we will examine their group of “symmetries” and the space that has a larger group of symmetries would be more symmetrical. We will regard area-preserving piecewise-linear self-homeomorphisms as “symmetries”. We will also compare the group of “symmetries” of surface of a cube with two-dimensional sphere. In the end, we will ask a question about the structure of the area-preserving self maps of two dimensional sphere and we will examine similar questions in the three dimensional case.
Rastegar, A. (2022). Circle or Square, Which One Is More Symmetrical?. Mathematical Culture and Thought, 40(2), 79–85. https://doi.org/10.30504/mct.2022.324
MLA
Rastegar, A. "Circle or Square, Which One Is More Symmetrical?", Mathematical Culture and Thought, 40, 2, 2022, 79–85. doi: 10.30504/mct.2022.324
HARVARD
Rastegar, A. (2022). 'Circle or Square, Which One Is More Symmetrical?', Mathematical Culture and Thought, 40(2), pp. 79–85. doi: 10.30504/mct.2022.324
CHICAGO
Rastegar, A., "Circle or Square, Which One Is More Symmetrical?." Mathematical Culture and Thought, 40 2 (2022): 79–85, doi: 10.30504/mct.2022.324
VANCOUVER
Rastegar A. Circle or Square, Which One Is More Symmetrical?. An Expository Journal of the Iranian Mathematical Society. 2022;40(2):79–85 (In Persian). doi: 10.30504/mct.2022.324
