GENERAL: Basic Mathematics!

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

Return-path: <[email protected]>
Return-path: owner-geodesic <@PSUVM.PSU.EDU:owner-geodesic@xxxxxxxxxxxxxxxxxxx>
Received: from Jnet-DAEMON by ARCH.PSU.EDU (PMDF #12866) id
<01H6ATY5O9KW96VJZ1@xxxxxxxxxxxx>; Fri, 10 Dec 1993 03:48 EDT
Received: From PSUVM(MAILER) by PSUARCH with Jnet id 3742 for HRL@PSUARCH; Fri,
10 Dec 1993 03:48 EST
Received: from PSUVM.PSU.EDU (NJE origin LISTSERV@PSUVM) by PSUVM.PSU.EDU
(LMail V1.1d/1.7f) with BSMTP id 1038; Fri, 10 Dec 1993 03:48:42 -0500
Date: Fri, 10 Dec 1993 00:48:21 -0800
From: 4D Solutions <pdx4d@xxxxxxxxxxx>
Subject: Volume of a Tetrahedron
Sender: List for the discussion of Buckminster Fuller's works
<[email protected]>
To: Multiple recipients of list GEODESIC <[email protected]>
Reply-to: List for the discussion of Buckminster Fuller's works
<[email protected]>
Message-id: <01H6ATY5O9KW96VJZ1@xxxxxxxxxxxx>
X-To: GEODESIC@xxxxxxxxxxxxxxxxxxx

>>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 . >roller@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

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
pdx4d@xxxxxxxxxxx
Partial thread listing: