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Topic: A Theorem concerning the Trisectors of a Triangle
Replies: 24   Last Post: Nov 10, 1998 12:19 AM

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 John Conway Posts: 2,238 Registered: 12/3/04
Re: A Theorem concerning the Trisectors of a Triangle
Posted: Sep 20, 1998 12:50 PM

> eleven smaller tetrahedra as follows:
> 1. {C1, C2, C3, C4}.> 2. {C1, C2, C3, V4}.> 3. {C1, C2, C4, V3}.
> 7. {C2, C3, V1, V4}.> 8. {C3, C4, V1, V2}.> 9. {C1, C3, V2, V4}.
> 10. {C1, C4, V2, V3}.> 11. {C2, C4, V1, V3}.

> The question is, whether in general it is even possible for the four
> tetrahedra which share one of the vertices of {V1, V2, V3, V4}, to be of
> equal volume. For instance, numbers 5, 7, 8, and 11 of the list above share
> vertex V1. Perhaps it is true that the *regions they represent* do have
> equal volumes; for if one takes a section of the large tetrahedron, {V1,
> V2, V3, V4},by a plane containing the triangle {C2, C3, C4}, and allows it
> to cut off the four tetrahedra meeting at V1, then, I think, the four
> triangles in the section are similar, and have equal area, and the height
> to V1 is the same for all of them. Maybe.

Sorry my previous message was incomplete. This configuration looks
interesting - I'll study it.

John Conway

Date Subject Author
9/12/98 Den Roussel
9/12/98 John Conway
9/13/98 Larry Cusick
10/27/98 John Conway
9/13/98 steve sigur
9/14/98 John Conway
9/15/98 John Conway
9/15/98 Richard Guy
9/15/98 John Conway
9/15/98 Richard Guy
9/15/98 Richard Guy
9/16/98 Floor van Lamoen
9/16/98 John Conway
9/17/98 Floor van Lamoen
9/17/98 John Conway
9/17/98 Floor van Lamoen
9/17/98 Russell Towle
9/17/98 John Conway
9/17/98 Russell Towle
9/17/98 Douglas J. Zare
9/19/98 Russell Towle
9/20/98 John Conway
9/20/98 John Conway
9/18/98 Antreas P. Hatzipolakis
11/10/98 Den Roussel