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Rational Trigonometry in Higher Dimensions and a Diagonal Rule for 2-planes in Four-dimensional space
Norman J Wildberger
; School of Mathematics and Statistics UNSW, Sydney, Australia
Puni tekst: engleski, pdf (203 KB)
Wildberger, N.J. (2017). Rational Trigonometry in Higher Dimensions and a Diagonal Rule for 2-planes in Four-dimensional space. KoG, 21(21), 47-54. Preuzeto s https://hrcak.srce.hr/192231
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.
rational trigonometry; subspaces; canonical angles; Diagonal rule; spread; cross
Hrčak ID: 192231
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