Re: Every convex quadrilateral a perspective image of a rectangle?

From: Narasimham G.L. (mathma18_at_hotmail.com)
Date: 10/06/04 

Date: 6 Oct 2004 03:54:52 -0700

"William McWorter" <mcworter@midohio.net> wrote in message news:<DyV8d.12$Rw6.7@news.ee.net>...
> Alexander Bogomolny showed me how every convex quadrilateral can be a
> perspective image of a parallelogram; that is, for any pyramid with a convex
> quadrilateral base, there is a slice through the pyramid which is a
> parallelogram. Given a convex quadrilateral, can one choose a pyramid with
> the given quadrilateral as base such that there exists a slice through that
> pyramid which is a rectangle?
> William

Generally perhaps no. Right(not oblique) pyramids of symmetrical
trapezium base are an obvious special case.

Also a rectangle section is a special case of a parallelogram section.
This question can be answered if, from the earlier (projective
geometry?) work, an expression for one angle of the parallelogram can
be extracted from symbolic data of {convex quadrilateral base
vertices, pyramid vertex and slicing plane inclination}.

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