GENERAL: Basic Mathematics!

From: IN%"[email protected]" "List for the discussion of Buckminster
Fuller's works" 10-DEC-1993 03:48:41.65
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Subj: Volume of a Tetrahedron

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From: 4D Solutions <[email protected]>
Subject: Volume of a Tetrahedron
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>>By the way, there *is* a formula the provides the volume of
>>*any* tetrahedron given its 6 edges as inputs. It's a monster
>>formula, derived by Leonhard Euler. I doubt I could write it
>>understandably in ASCII.
>
>let ABCD be a tetrahedron with sides
>
> a = AD, b = BD, c = CD,
> p = BC, q = CA, r = AB.
>
>The volume V of the tetrahedron can be computed
>from the determinant of a 5-by-5 matrix as follows
>(here ^2 means taking squares).
>
> | 0 r^2 q^2 a^2 1|
> | |
> |r^2 0 p^2 b^2 1|
> | |
> 288 V^2 = |q^2 p^2 0 c^2 1|
> | |
> |a^2 b^2 c^2 0 1|
> | |
> | 1 1 1 1 0|
>
>--
>Martin Roller, Mathematik, . Tel +49 941 943 2991
>Universitaet Regensburg, . Fax +49 941 943 2576
>93040 Regensburg, Germany . >[email protected]

Cool! I never saw that one before. I look forward
to trying it out.

>Does anybody know Fuller's precise calculations for the structural
>stability of domes or more details of Otto's case against it? Who is >right?

That's a good question! I don't have the answer but I will
help circulate your query.

-- Kirby
[email protected]
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