Abstract
A theorem of Liouville asserts that the simplest angle-preserving transformations on Euclidean space—translations, dilations, reflections, and inversions—generate all angle-preserving transformations when the dimension is at least 3. This note gives a proof which uses only elementary multivariable calculus and simplifies a differential-geometric argument of Flanders.
MSC:
ACKNOWLEDGMENT
The authors are grateful to Farhan Abedin for comments and suggestions on an earlier draft of this note, and in particular for suggesting to include Proposition 4.
DISCLOSURE STATEMENT
No potential conflict of interest was reported by the author(s).