The discussion centers on the group of symmetries of a rectangle, particularly focusing on the nature of reflections and rotations. Participants explore why a rectangle has only two reflection symmetries compared to a square, and the implications of reflecting a rectangle over its diagonals.
Participants express differing views on the nature of reflections and rotations in relation to the rectangle's symmetry. There is no consensus on the reasons behind the limited reflections or the effects of diagonal reflections.
Participants reference external resources for visual aids, indicating that understanding may depend on specific definitions and interpretations of symmetry. The discussion does not resolve the mathematical or conceptual uncertainties raised.
This discussion may be of interest to individuals studying geometry, particularly those exploring symmetry, transformations, and the properties of shapes like rectangles and squares.
LagrangeEuler said:Why group of symmetry of rectangle does not have more reflections but only two. Why does not have reflections over diagonal as in case of square? Thanks for the answer.
http://mathonline.wikidot.com/the-group-of-symmetries-of-a-rectangle
Yes, that's true. But what happens if you add an orientation, a tiny arrow which shows a direction you could walk along the rectangle? Then you see, that rotation and reflection are different, although the non-oriented figure is the same. (Not important to your original question though, but useful to remember.)LagrangeEuler said:I don't not why
http://mathonline.wikidot.com/the-group-of-symmetries-of-a-rectangle
If I look figure here rotation by 180 degrees will be symmetry.