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Does anybody know of a book containing "all you want to know about the tetrahedron"? What you want to know should include basic geometry of the tetrahedron, study of orthocentric tetrahedra, the Monge point, various volume / edge length / face area formulae, volume via the Cayley-Menger determinant, the regular tetrahedron, etc.

The wikipedia page for "tetrahedron" is fairly interesting, but it will never treat things with the same level of detail as a textbook.

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    $\begingroup$ all you want to know about the tetrahedron <i>but were afraid to ask</i>? $\endgroup$ – Anthony Quas Jun 18 '15 at 8:35
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Asking Math Reviews for books with "tetrahedr*" in the title turned up a couple of possibilities.

Anđelko Marić, Tetrahedron. Definitions, theorems, formulas, problems. Translated by Juraj Šiftar. Publishing House ELEMENT, Zagreb, 2010. 176 pp. ISBN: 978-953-197-580-3, MR2963754.

Kesiraju Satyanarayana, Angles and in- and ex-elements of triangles and tetrahedra. Studies in coordinate geometry with introductory results on determinants, linear equations, change of reference simplex, tetrahedra, etc. Bangalore Press, Bangalore City 1962 xiii+135 pp, MR0157268 (28 #504).

Also, this, but with no further information given:

Dov Jarden, The tetrahedron: A collection of papers. Published by the author, Jerusalem 1963 41 pp, MR0149341 (26 #6831).

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  • $\begingroup$ Thank you! These books seem interesting, especially the first. Now comes the question: how can I put my hands on it? It's not in my local library and I can't even seem to find it for sale somewhere on the web... $\endgroup$ – Matthieu Romagny Jun 18 '15 at 7:17
  • $\begingroup$ There's a website element.hr/artikli/440/tetrahedron that might help if you can get through to it, but I keep getting an error message. $\endgroup$ – Gerry Myerson Jun 18 '15 at 7:22
  • $\begingroup$ Yes, that's the website of the publisher in Zagreb, Croatia. I sent a mail there to see if there is a way to buy the book. Thanks, $\endgroup$ – Matthieu Romagny Jun 18 '15 at 8:16
  • $\begingroup$ Indeed there is a way - I'll buy the book and see. $\endgroup$ – Matthieu Romagny Jun 18 '15 at 11:55
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Perhaps someone who reads Russian can comment on whether or not this might help answer the OP's query:

Ya.P.Ponarin. Elementary Geometry. Triangles and tetrahedra / Elementarnaya geometriya. Treugolniki i tetraedry. 2009.


          Cover
         


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  • $\begingroup$ Seems interesting indeed... $\endgroup$ – Matthieu Romagny Jun 18 '15 at 11:55

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