advanced_tools:group_theory
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advanced_tools:group_theory [2018/03/28 16:23] jakobadmin [Intuitive] |
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| Obvious examples of such transformations are rotations, by $90^\circ$, $180^\circ$, $270^\circ$, and of course $0^\circ$. | Obvious examples of such transformations are rotations, by $90^\circ$, $180^\circ$, $270^\circ$, and of course $0^\circ$. | ||
| - | {{:advanced_tools:einheitsquadrat-gedreht22-150x150.png?nolink|}} | + | {{ :advanced_tools:einheitsquadrat-gedreht22-150x150.png?nolink|}} |
| A counter-example is a rotation by, say $5^\circ$. The upper-right corner point $A$ of the square is obviously mapped to a point $A'$ outside of the initial set. Of course, a square still looks like a square after a rotation by $5^\circ$, but, by definition, this is a different square, mathematically a different set of points. Hence, a rotation by $5^\circ$ is no symmetry of the square. | A counter-example is a rotation by, say $5^\circ$. The upper-right corner point $A$ of the square is obviously mapped to a point $A'$ outside of the initial set. Of course, a square still looks like a square after a rotation by $5^\circ$, but, by definition, this is a different square, mathematically a different set of points. Hence, a rotation by $5^\circ$ is no symmetry of the square. | ||
advanced_tools/group_theory.txt · Last modified: 2020/09/07 05:18 by 14.161.7.200
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