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

Fulltext: english, pdf (203 KB) pages 47-54 downloads: 464* cite
APA 6th Edition
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. https://doi.org/10.31896/k.21.2
MLA 8th Edition
Wildberger, Norman J. "Rational Trigonometry in Higher Dimensions and a Diagonal Rule for 2-planes in Four-dimensional space." KoG, vol. 21, no. 21, 2017, pp. 47-54. https://doi.org/10.31896/k.21.2. Accessed 25 Nov. 2020.
Chicago 17th Edition
Wildberger, Norman J. "Rational Trigonometry in Higher Dimensions and a Diagonal Rule for 2-planes in Four-dimensional space." KoG 21, no. 21 (2017): 47-54. https://doi.org/10.31896/k.21.2
Harvard
Wildberger, N.J. (2017). 'Rational Trigonometry in Higher Dimensions and a Diagonal Rule for 2-planes in Four-dimensional space', KoG, 21(21), pp. 47-54. https://doi.org/10.31896/k.21.2
Vancouver
Wildberger NJ. Rational Trigonometry in Higher Dimensions and a Diagonal Rule for 2-planes in Four-dimensional space. KoG [Internet]. 2017 [cited 2020 November 25];21(21):47-54. https://doi.org/10.31896/k.21.2
IEEE
N.J. Wildberger, "Rational Trigonometry in Higher Dimensions and a Diagonal Rule for 2-planes in Four-dimensional space", KoG, vol.21, no. 21, pp. 47-54, 2017. [Online]. https://doi.org/10.31896/k.21.2

Abstracts
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

[croatian]

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