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Topic: Common Core snippet a little distressing
Replies: 73   Last Post: Jul 26, 2013 6:27 PM

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 kirby urner Posts: 3,690 Registered: 11/29/05
Re: Common Core snippet a little distressing
Posted: Jul 16, 2013 7:52 PM
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On Tue, Jul 16, 2013 at 4:42 PM, Wayne Bishop <wbishop@calstatela.edu>wrote:

> At 06:55 AM 7/15/2013, kirby urner wrote:
>
> As to how to duplicate a tetrahedron with a ruler and compass in 3D if

>> that's what's asked, it sounds doable, but not in a way I'd want to try
>> typing out in words here. Sounds like a CAD challenge of some kind.
>>

>
> Assuming the traditional straightedge (Ax 1: Two points determine a line)
> as opposed to a "ruler", I am sure it is not, and fairly easily reducible
> to the traditional solution (or NON-solution, if you prefer), the
> irreducibility of p(x) = x^3 - 2 over the integers (rationals, if you
> prefer). You know, the contrapositive,"If the edge of a regular
> tetrahedron could be constructed with compass and straightedge that is the
> edge of a regular tetrahedron of double the volume of the original, then?"
>
> Wayne
>
>
>

Yes, my apologies, not a "ruler" per se. My understanding is that, in
practice, a straight edge was presented, as often as not, by a taut string,
something easily carried around coiled up, yet usable for drawing any arcs
or circles, so it's your compass as well (given line segments of 1/n
subtend angles in proportion). Any cube contains a tetrahedron 1/3rd its
volume as a set of face diagonals (two tetrahedra comprise all 12
diagonals) so whatever construction works or doesn't (if you prefer) in
creating a cube with an edge/compass would have its associated tetrahedron
implied.

Kirby

Date Subject Author
7/13/13 Peter Duveen
7/13/13 Robert Hansen
7/13/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/15/13 kirby urner
7/14/13 Wayne Bishop
7/14/13 kirby urner
7/14/13 Wayne Bishop
7/15/13 kirby urner
7/15/13 Robert Hansen
7/15/13 Christian Baune
7/15/13 kirby urner
7/16/13 Wayne Bishop
7/16/13 kirby urner
7/14/13 Wayne Bishop
7/14/13 Joe Niederberger
7/15/13 Joe Niederberger
7/15/13 Joe Niederberger
7/15/13 Robert Hansen
7/15/13 kirby urner
7/15/13 Robert Hansen
7/16/13 kirby urner
7/16/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/15/13 CCSSIMath
7/16/13 Joe Niederberger
7/16/13 Robert Hansen
7/16/13 kirby urner
7/17/13 Joe Niederberger
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 kirby urner
7/17/13 Robert Hansen
7/18/13 Wayne Bishop
7/17/13 Joe Niederberger
7/17/13 Joe Niederberger
7/17/13 Robert Hansen
7/18/13 Wayne Bishop
7/18/13 Joe Niederberger
7/18/13 kirby urner
7/18/13 Joe Niederberger
7/20/13 kirby urner
7/19/13 Joe Niederberger
7/19/13 kirby urner
7/19/13 Joe Niederberger
7/19/13 Joe Niederberger
7/20/13 kirby urner
7/21/13 Joe Niederberger
7/23/13 kirby urner
7/24/13 frank zubek
7/24/13 frank zubek
7/24/13 kirby urner
7/25/13 frank zubek
7/25/13 kirby urner
7/25/13 frank zubek
7/25/13 frank zubek
7/25/13 frank zubek
7/26/13 frank zubek
7/26/13 frank zubek

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