Week 6
Beyond flatland:
More about motions on Euclidean space
This week, I discuss the classification of Euclidean motions
in arbitrary dimensions and some applications of Euclidean geometry.
I prove that in any dimension,
reflections generate all motions on Euclidean space.
This in particular leads to a second proof for the classification of motions
on E2.
Finally, I'll prove some well-known theorems from plane geometry by
applying the results obtained so far.
Helpful literature:
-
M. Reid, Geometry and Topology, chapters of forthcoming
textbook by M. Reid and B. Szendröi, available from General Office:
Sections 2.14 and 3.