Find the number of isometries of the brick.
Consider a brick of length $3 cm$ ,breadth $=2$ cm and height $=1$ cm
Find the number of isometries of the brick.
I know that isometry means distance preserving metrics.But how to find the number of metrics which preserve distances
Please help.
metric-spaces isometry
asked Nov 28 '18 at 17:15
Join_PhDJoin_PhD
3068
add a comment |
Consider a brick of length $3 cm$ ,breadth $=2$ cm and height $=1$ cm
Find the number of isometries of the brick.
I know that isometry means distance preserving metrics.But how to find the number of metrics which preserve distances
Please help.
metric-spaces isometry
asked Nov 28 '18 at 17:15
Join_PhDJoin_PhD
3068
turn it around in appropriate ways -- this you can simulate with a real brick. Then consider reflections mapping the brick to itself (which you cannot realize with a real brick)
– Thomas
Nov 28 '18 at 17:18
Look at the extremal points / vertices, this is a finite set, an isometry induces a permutation of them, and there are not so many. Insist first that such a permutation preserves distances...
– dan_fulea
Nov 28 '18 at 17:19
add a comment |
Consider a brick of length $3 cm$ ,breadth $=2$ cm and height $=1$ cm
Find the number of isometries of the brick.
I know that isometry means distance preserving metrics.But how to find the number of metrics which preserve distances
Please help.
metric-spaces isometry
asked Nov 28 '18 at 17:15
Join_PhDJoin_PhD
3068
Consider a brick of length $3 cm$ ,breadth $=2$ cm and height $=1$ cm
Find the number of isometries of the brick.
I know that isometry means distance preserving metrics.But how to find the number of metrics which preserve distances
Please help.
metric-spaces isometry
metric-spaces isometry
asked Nov 28 '18 at 17:15
Join_PhDJoin_PhD
3068
asked Nov 28 '18 at 17:15
Join_PhDJoin_PhD
3068
asked Nov 28 '18 at 17:15
Join_PhDJoin_PhD
3068
asked Nov 28 '18 at 17:15
Join_PhDJoin_PhD
3068
asked Nov 28 '18 at 17:15
Join_PhDJoin_PhD
3068
3068
turn it around in appropriate ways -- this you can simulate with a real brick. Then consider reflections mapping the brick to itself (which you cannot realize with a real brick)
– Thomas
Nov 28 '18 at 17:18
Look at the extremal points / vertices, this is a finite set, an isometry induces a permutation of them, and there are not so many. Insist first that such a permutation preserves distances...
– dan_fulea
Nov 28 '18 at 17:19
add a comment |
turn it around in appropriate ways -- this you can simulate with a real brick. Then consider reflections mapping the brick to itself (which you cannot realize with a real brick)
– Thomas
Nov 28 '18 at 17:18
Look at the extremal points / vertices, this is a finite set, an isometry induces a permutation of them, and there are not so many. Insist first that such a permutation preserves distances...
– dan_fulea
Nov 28 '18 at 17:19
turn it around in appropriate ways -- this you can simulate with a real brick. Then consider reflections mapping the brick to itself (which you cannot realize with a real brick)
– Thomas
Nov 28 '18 at 17:18
turn it around in appropriate ways -- this you can simulate with a real brick. Then consider reflections mapping the brick to itself (which you cannot realize with a real brick)
– Thomas
Nov 28 '18 at 17:18
Look at the extremal points / vertices, this is a finite set, an isometry induces a permutation of them, and there are not so many. Insist first that such a permutation preserves distances...
– dan_fulea
Nov 28 '18 at 17:19
Look at the extremal points / vertices, this is a finite set, an isometry induces a permutation of them, and there are not so many. Insist first that such a permutation preserves distances...
– dan_fulea
Nov 28 '18 at 17:19
add a comment |
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turn it around in appropriate ways -- this you can simulate with a real brick. Then consider reflections mapping the brick to itself (which you cannot realize with a real brick)
– Thomas
Nov 28 '18 at 17:18
Look at the extremal points / vertices, this is a finite set, an isometry induces a permutation of them, and there are not so many. Insist first that such a permutation preserves distances...
– dan_fulea
Nov 28 '18 at 17:19