Re: Determinants and area

From: Lee Rudolph (lrudolph_at_panix.com)
Date: 03/17/05 

Date: 17 Mar 2005 18:31:03 -0500

"Dani" <tictactictac@walla.co.il> writes:

[in public, at last!]

>Anyway, here what I wrote:
...
>But isn't there any way to define the volume of polytopes by some
>finite sum? for instance, (a) finding representatives from a few Dehn
>classes that together generate by dissection and disjoint union the set
>of polytopes with rational volume?

Do you have reason to believe that "a few" such classes exist?
I haven't thought about this deeply ever, or at all recently,
but offhand I see no reason to believe that you don't need
uncountably many "Dehn classes" to "together generate by dissection
and disjoint union the set of polytopes with rational volume".

Lee Rudolph