(This is a partial copy, from enwiki, to test formatting here.)

March 4[edit]

What did von Neumann's variant of von Neumann–Bernays–Gödel set theory look like?[edit]

The "History" section of our article on von Neumann–Bernays–Gödel set theory starts with "The first variant of NBG, by John von Neumann in the 1920s, took functions and not sets, as primitive," without further elaboration, and the set theory books I have seen usually do not go into von Neumann's original conception at all, leaving me with the question, what did von Neumann's variant of NBG look like? — Tobias Bergemann (talk) 13:11, 4 March 2013 (UTC)[reply]

Doubling the cube[edit]

Can anyone explain me in simple maths that the neusis construction at http://en.wikipedia.org/wiki/Doubling_the_cube#Using_a_marked_ruler why equals cuberoot2? 117.233.117.95 (talk) 13:34, 4 March 2013 (UTC)[reply]

(Image copied here for ease of reference.) There's a proof here ("Construction 3", starting on page 7 of the PDF) of what appears to be the same construction, though I haven't worked through it yet. AndrewWTaylor (talk) 17:10, 4 March 2013 (UTC)[reply]

Penrose tiles puzzle pieces[edit]

Does anyone have any suggestions on a set of Penrose tiles jigsaw puzzle pieces. They're for my nephew. (Well, really they're for me... :-) Sławomir Biały (talk) 23:31, 4 March 2013 (UTC)[reply]

A classic interlocking jigsaw puzzle would not follow the boundaries of Penrose tiles. You could do that, but why not get actual Penrose tiles and assemble them yourself into what ever size Penrose pattern you want ? (Instead of buying the tiles, you could also cut them out of construction paper.) Note that patchwork quilts are sometimes made in such a way, so, if either of you are interested in sewing, that's a more practical application, starting from fabric "cells": [1]. StuRat (talk) 01:43, 6 March 2013 (UTC)[reply]

Yes, I'm looking for a good set of tiles that fit together, maybe with some kind of edge matching as explained in the article. I don't want to cut them out myself, as I lack the patience for it. Sławomir Biały (talk) 16:47, 6 March 2013 (UTC)[reply]

What about http://www.gamepuzzles.com/pentuniv.htm#TD? Maybe that contains something? -- Toshio Yamaguchi 12:57, 7 March 2013 (UTC)[reply]

March 5[edit]

A maximum/minimum value question[edit]

Dear Wikipedians:

A question calls for the finding of the absolute maximum and minimum value of $f(x,y,z)=x^{2}+y^{2}+z^{2}$ subject to the constraints $x-y=1$ and $y^{2}-z^{2}=1$

Using Lagrange multipliers, I set up the following function:

(start preformatted section as 13 seconds faster):

<pre>

$L(x,y,z,\lambda ,\mu )=x^{2}+y^{2}+z^{2}+\lambda (x-y-1)+\mu (y^{2}-z^{2}-1)$

Setting the first partial derivatives of L to zero, we obtain

$2x+\lambda =0$	(1)
$2y-\lambda +2\mu y=0$	(2)
$2z-2\mu z=0$	(3)
$x-y-1=0$	(4)
$y^{2}-z^{2}-1=0$	(5)

From (3) I find $\mu =1$ , substituting into (2):

$2y-\lambda +2y=0$

$\lambda =4y$ (6)

Substituting (6) into (1):

$2x+4y=0$

$x=-2y$ (7)

Substituting (7) into (4):

$-2y-y-1=0$

$-3y=1$

$y=-{\frac {1}{3}}$

Substituting $y=-{\frac {1}{3}}$ into (5):

$\left(-{\frac {1}{3}}\right)^{2}-z^{2}-1=0$

$z^{2}=-{\frac {8}{9}}$

(end preformatted section)

This means that there are no real solutions to the original problem. However the official solutions clearly indicate the existence of real solutions. I am wondering what is going on?

Thanks for all your help. </nowiki> 74.14.60.239 (talk) 02:42, 5 March 2013 (UTC)[reply]