Original scientific paper

https://doi.org/10.31896/k.21.2

Rational Trigonometry in Higher Dimensions and a Diagonal Rule for 2-planes in Four-dimensional space

Norman J Wildberger orcid.org/0000-0003-3503-6495 ; School of Mathematics and Statistics UNSW, Sydney, Australia

Abstract

We extend rational trigonometry to higher dimensions by introducing rational invariants between k-subspaces of n-dimensional space to give an alternative to the canonical or principal angles studied by Jordan and many others, and their angular variants. We study in particular the cross, spread and det-cross of 2-subspaces of four-dimensional space, and show that Pythagoras theorem, or the Diagonal Rule, has a natural generalization for such 2-subspaces.

Keywords

rational trigonometry; subspaces; canonical angles; Diagonal rule; spread; cross

Hrčak ID:

192231

URI

https://hrcak.srce.hr/192231

Publication date:

9.1.2018.

Article data in other languages: croatian

Visits: 1.652 *