1. Mathematics
2. Geometry and Topology
3. Synthetic Geometry
4. 52031

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:

.

Attachments

• metrics 4.doc