Talk:Euler brick

message: I believe the conditions on the edges given for a perfect cuboid apply to all Euler bricks. Also a perfect cuboid must have edges divisible by 7 and 19. Ringman8567 (talk) 18:13, 28 January 2008 (UTC)
thread_title: old thread

message: Some interesting facts about a perfect cuboid.
* 2 edges must be even and 1 edge must be odd (for a primitive perfect cuboid).
* 1 edge must be divisible by 4 and 1 edge must be divisible by 16
* 1 edge must be divisible by 3 and 1 edge must be divisible by 9
* 1 edge must be divisible by 5
* 1 edge must be divisible by 11
I think this must be a mistake. See this page on f2.org. It says, those are "Some properties of primitive Euler bricks"! In fact, primitive Euler bricks are not same as Euler bricks or perfect cuboid!
--Cnchina (talk)  —Preceding comment was added at 01:38, 17 July 2008 (UTC)
replies: text: Actually, if the perfect cuboid exists, it will be a primitive Euler Brick, so it does in fact share the same properties.  If I remember it right, a primitive Euler brick is one with sides whose gcf is 1.  So the facts are correct.TheRingess (talk) 06:13, 17 July 2008 (UTC)
replies: text: It's not true that all perfect cuboids are primitive Euler Bricks. If (a,b,c) is a perfect cuboid, then (2a,2b,2c) is also a perfect cuboid, but isn't primitive. Perhaps you mean "If a perfect cuboid exists, then a primitive perfect cuboid also exists"? This would be true, since any non-primitive could be converted to a primitive by dividing out the gcd. Staecker (talk) 11:23, 28 July 2009 (UTC)
thread_title:  Facts? 

message: I believe the name Euler is pronounced the same as "oiler", so the indefinite article should be "an", not "a".  Comments?—GraemeMcRaetalk 18:42, 10 April 2009 (UTC)
thread_title:  a Euler brick vs. an Euler brick 

message: :a_1^2 + a_2^2 + a_3^2\ =\ c^2\ =\ \frac{b_1^2 + b_2^2 + b_3^2}{2}
Now, if only someone were to show that the sum of three non-zero perfect squares can never be both a perfect square itself, and the semi-sum of other three non-zero perfect squares at the same time... — 79.113.221.97 (talk) 01:17, 20 March 2013 (UTC)
replies: text: If you are referring to the above discussion about primitive vs non-primitive Euler Bricks, your equation should be something like a_1^2 + a_2^2 + a_3^2\ =\ c^2\ =\ \frac{b_1^2 + b_2^2 + b_3^2}{4} where b_1 = 2*a_1, b_2 = 2*a_2, b_3 = 2*a_3. Nothing to prove there.TheRingess (talk) 04:09, 20 March 2013 (UTC)
replies: text: No, that's not what I'm talking about. When you add the squares of the three diagonals together, you get twice the sum of the squares of the three edges, which itself is the square of the main diagonal. — 79.113.221.97 (talk) 04:22, 20 March 2013 (UTC)
replies: text: Okay.  Maybe someone will prove it some day.TheRingess (talk) 07:14, 20 March 2013 (UTC)
replies: text: No, this is not equivalent -- you've lost important information relating your as and bs.  For example, try "edges" of lengths 1,2,2, "diagonals" of lengths 1,1,4, and "space diagonal" of length 3: these numbers satisfy your equations but don't yield an Euler birch. --JBL (talk) 14:07, 20 March 2013 (UTC)
replies: text: I never said that they are "equivalent"... merely that the former implies the latter. So, if the latter would be proven untrue, so would that which gave birth to it. Reduction to the absurd. — 79.113.214.121 (talk) 16:41, 20 March 2013 (UTC)
replies: text: sigh .  Anonymous, Joel B just showed you that your statement as written is false.  He showed you that the sum of 3 non zero perfect squares 1 + 4 + 4 = 9, and 9 is a perfect square, can also be written as the semi-sum of other three non zero perfect squares (9 = (1 + 1 + 16)/2).  Therefore your theoem as written is false.  There's no reduction to the absurd, nothing like that, merely a counter example that disproves the theorm.TheRingess (talk) 04:12, 21 March 2013 (UTC)
replies: text: OK. Thanks. — 79.113.214.121 (talk) 05:56, 21 March 2013 (UTC)
thread_title:  In other words... 

message: Currently at the end of the article is the sentence
:Solutions [for a perfect parallelepiped] with only a single oblique angle have been found.
Taken literally this cannot be true, since each face is a quadrilateral and no quadrilateral has only a single oblique angle. Can someone clarify in the article?  Loraof (talk) 16:40, 30 March 2015 (UTC)
thread_title:  Unclear sentence 

message: https://arxiv.org/abs/1506.02215  — Preceding unsigned comment added by 188.146.74.175 (talk) 12:53, 12 March 2017 (UTC)
replies: text: arXiv has no peer review and is not by itself an acceptable source for Wikipedia. See Wikipedia:Reliable source examples#arXiv preprints and conference abstracts. PrimeHunter (talk) 13:09, 12 March 2017 (UTC)
replies: text: The correctness of Walter Wyss's proof is disputed by Ruslan Sharipov in . Chris Thompson (talk) 14:23, 22 May 2018 (UTC)
replies: text:  We've already gone a circle of this before; see the article history from March 2017 as well as e.g. this thread on my talkpage.  It was briefly and regrettably added to the article then, and removed within two weeks; there is no reason at all to think the arXiv posting is a valid proof of anything. --JBL (talk) 14:33, 22 May 2018 (UTC)

text: Nothing about that preprint is even vaguely promising. JBL (talk) 18:34, 12 November 2022 (UTC)
replies: text: I see. The paper shows this method of constructing a perfect parallelepiped from Pythagorean triple cannot yield perfect cuboid, and even if it showed this applies to all Pythagorean triples, Pythagorean triples don't cover the whole space of perfect parallelepipeds, so the claim of proof of nonexistence of perfect cuboid is wrong by incompleteness. 104.246.130.239 (talk) 05:59, 5 December 2022 (UTC)
thread_title:  Proven? 

message: Too specific a subtopic to stand alone. –LaundryPizza03 (dc̄) 15:08, 2 October 2020 (UTC)
replies: text: Klbrain (talk) 11:01, 1 May 2021 (UTC)
thread_title:  Proposed merge of [[Cuboid conjectures]] into [[Euler brick]] 

message: Article says "Only recently have cuboids in complex numbers become known." However, I have a query, what are Euler bricks called if they are expressed in https://en.wikipedia.org/wiki/Non-integer_base_of_numeration ?
I've tried googling, but, maybe I am just really naive, and there is no such thing?
Thank you to any Wikipedian who can answer this query. 49.185.41.142 (talk) 20:24, 2 May 2022 (UTC)
replies: text: The property of a length to be an integer or not does not depend on the base of numeration that is used to represent numbers. So, "expressing Euler bricks in non-integer base of numeration" is nonsensical. D.Lazard (talk) 06:43, 3 May 2022 (UTC)
thread_title:  Naive question