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Remembering spherical trigonometry

Published online by Cambridge University Press:  14 March 2016

John Conway  and
Alex Ryba
John Conway
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ, USA
Alex Ryba
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ, USA
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Extract

Although high school textbooks from early in the 20th century show that spherical trigonometry was still widely taught then, today very few mathematicians have any familiarity with the subject. The first thing to understand is that all six parts of a spherical triangle are really angles — see Figure 1.

This shows a spherical triangle ABC on a sphere centred at O. The typical side is a = BC is a great circle arc from to that lies in the plane OBC; its length is the angle subtended at O. Similarly, the typical angle between the two sides AB and AC is the angle between the planes OAB and OAC.

Type
Research Article
Information
The Mathematical Gazette , Volume 100 , Issue 547 , March 2016 , pp. 1 - 8
Copyright
Copyright © Mathematical Association 2016 

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References

1.Napier, J., Mirifici logarithmorum canonis descriptio, Hart, Edinburgh (1614).Google Scholar
2.Sylvester, J. J., Note on a memoria technica for Delambre's, commonly called Gauss's theorems, Philosophical Magazine, Series 4, Volume 32 (1866) pp. 436–438.Google Scholar
3.Workman, W. P., Memoranda Mathematica, Clarendon Press, Oxford (1912).Google Scholar
4.Smart, W. M., Textbook on spherical astronomy, (5th edn.), Cambridge University Press (1971) [the first edition was 1928].Google Scholar
5.Todhunter, I., Note on the history of certain formulae in spherical trigonometry, Philosophical Magazine, Series 4, Volume 45 (1873) pp. 98–100.Google Scholar
6.Conway, J. H. and Ryba, A., Fibonometry, Math. Gaz. 97(November 2013) pp. 494–495.CrossRefGoogle Scholar
7.Osborn, G., Mnemonic for hyperbolic formulae, Math. Gaz. 2 (July 1902) p. 189.Google Scholar
8.de Morgan, A., On the invention of circular parts, Philosophical Magazine, Series 3 Volume 22 (1843) pp. 350–353.Google Scholar