Euclidean Metric : Translation and Rotation
Let be the standard euclidean metric on defined by
where and are any points in .
a) a translation is a map given by
for some fixed given point . Prove, that the Euclidean metric d on is translation-invariant, ie, for any translation T it follows:
.
b) A rotation is a map given by
for some fixed real number . Prove, that the Euclidean metric d on is rotation-invariant, ie, for any rotation it follows:
.
© BrainMass Inc. brainmass.com October 9, 2019, 5:15 pm ad1c9bdddfhttps://brainmass.com/math/synthetic-geometry/euclidean-metric-translation-rotation-52031
Solution Preview
Please see the attached file for the complete solution.
Thanks for using BrainMass.
Let be the standard euclidean metric on defined by
where and are any points in .
a) a translation is a map given by
for some fixed ...
Solution Summary
Translation and rotation of a Euclidean metric are investigated. The solution is detailed and well presented.