Talk:Pythagorean tiling

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A fact from Pythagorean tiling appeared on Wikipedia's Main Page in the Did you know column on 24 October 2011 (check views). The text of the entry was as follows:

Did you know... that the Pythagorean tiling, a pattern of squares of two sizes that can be used to prove the Pythagorean theorem, appears in a painting (pictured) by Dutch Golden Age artist Jacob Ochtervelt?

A record of the entry may be seen at Wikipedia:Recent additions/2011/October. The nomination discussion and review may be seen at Template:Did you know nominations/Pythagorean tiling.

Wikipedia

I am standing on this right now

it can be split into substrings of the form "01" and "0" (that is, there are no two consecutive ones) and if these two substrings are consistently replaced by the shorter strings "0" and "1" then another string with the same structure results. I tried that on my tile floor that I am standing on now and got it. Turtleguy1134 (talk) 22:00, 23 October 2011 (UTC)[reply]

Proof of theorem

Here is a part of the current article:
"This tiling is called the Pythagorean tiling because it has been used as the basis of proofs of the Pythagorean theorem by the ninth-century Arabic mathematicians Al-Nayrizi and Thābit ibn Qurra, and by the 19th-century British amateur mathematician Henry Perigal".
Why not expose such a proof on "Pythagorean_theorem", where a link was just created to this article? 109.6.129.249 (talk) 16:22, 17 October 2012 (UTC)[reply]

On one hand, it is difficult to find this link to the article. On the other hand, the proof of the theorem given here is not clear. 109.6.129.249 (talk) 11:48, 18 October 2012 (UTC)[reply]

The article has been viewed 373 times in September. "Pythagorean_theorem" has been viewed 162696 times in the same month. The title "Pythagorean tiling" has no meaning for most people. It is not reasonable to expose within this article one proof or more of the theorem through a tiling.
109.6.129.249 (talk) 14:51, 31 October 2012 (UTC)[reply]

A click to go to "Pythagorean tiling" is scarce, and no source was given
to this title since the creation of the article. Moreover, no reason
to isolate on an article a partial proof of the Pythagorean theorem,
where a given right triangle is not isosceles. Really numerous
are proofs of the theorem through a tiling? At least one complete proof
through a tiling is logically expected below the title "Pythagorean theorem".
109.6.129.249 (talk) 15:18, 2 November 2012 (UTC)[reply]

The title is given in footnote [1] of the article, and has been since the creation of the article. And the article is not primarily about a particular proof of the Pythagorean theorem; that's one use of this tiling, and concerns one section of the article, but the tiling has other uses and properties described in the article's other sections. —David Eppstein (talk) 16:34, 2 November 2012 (UTC)[reply]

It is suggested that the section be merged…
109.6.129.249 (talk) 09:46, 3 November 2012 (UTC)[reply]

Many people could enjoy the image if inserted in a section about history of the Pythagorean theorem,

while it is difficult to know immediately what proofs are behind the image. Thus the author of the image

could be satisfied when the section will be removed.

194.153.110.5 (talk) 11:52, 7 November 2012 (UTC)[reply]

Speak for yourself. —David Eppstein (talk) 16:23, 7 November 2012 (UTC)[reply]

Speak for yourself, what does that mean? Do you think that this section of the article and its image
are revealing a principle of proofs of the theorem? What is the topic of this section of the article?
109.6.129.249 (talk) 13:34, 8 November 2012 (UTC)[reply]

A tiling by squares
is created from a right triangle. On the first row, three images show
a grid in dashed red which takes a particular position relative to the tiling.

It seems that, henceforth, the first image belongs to the article,
after four revocations. The fifth and last image is inserted
in the current section "Pythagorean theorem and dissections".
Image and section have a same author, who created the article.

At first the word "dissection" is used, its meaning is obscure.
Finally the author talks about a grid, but we see
no grid in the current section. Nothing is said about
a relation between the images of the first
and second sections.

Here is the last sentence in section "Pythagorean theorem and dissections":
"Similarly, overlaying two Pythagorean tilings may be used
to generate a six-piece dissection of two unequal squares
into a different two unequal squares". But nowhere
we see six pieces. Obviously we have
to improve the section.

194.153.110.5 (talk) 14:20, 27 November 2012 (UTC)[reply]

Oppose merger. I see no reason why this article should not mention that Pythagorean tilings have been used to prove Pythagoras' theorem. In fact, it seems perverse not to, since this is the very reason they are called Pythagorean tilings. As to whether the main article Pythagorean theorem should contain an independent discussion of this proof (that's not what "merge" means, by the way), that is an issue that should be discussed at Talk:Pythagorean theorem rather than here. In fact, there already is a section there responding to an earlier addition of content related to this proof to that page, and there seems to be no consensus to include it. Sławomir Biały (talk) 18:27, 29 November 2012 (UTC)[reply]
Oppose merger for basically the same reasons. I also oppose inclusion of symbol-packed images like "A pattern of Pythagorean tiling.svg" because I think all the formulas make it more confusing than helpful. —David Eppstein (talk) 23:30, 29 November 2012 (UTC)[reply]
Oppose merger. Even if there is a modest amount of overlap with the other page, this is quite common by wiki standards. Tkuvho (talk) 09:18, 30 November 2012 (UTC)[reply]

Additions to the page

Proposed additions to this page should be discussed here in small installments. Confrontational edits should be avoided. Tkuvho (talk) 17:24, 29 November 2012 (UTC)[reply]

About the suggestion to merge, see "Discuss"!
109.6.129.249 (talk) 17:41, 29 November 2012 (UTC)[reply]

But that's a link to the above discussion, which doesn't make any kind of case for a merger. The only pertinent comment there regarding a merger is my own "oppose" vote. Sławomir Biały (talk)

Please also note a possibly related discussion at Commons:Administrators' noticeboard/User problems#User:Baelde and Category:Pythagorean tiling. I am also opposed to any merger; I believe this is adequately notable as a standalone topic and that any inclusion of its content at the Pythagorean theorem article should have zero effect on what is included here. —David Eppstein (talk) 23:29, 29 November 2012 (UTC)[reply]

Six piece dissection of two squares into a different two squares

I think the article may already be a bit image heavy for the amount of text it has, so I'm reluctant to add this, but to the anonymous editor who was confused by the sentence in the article about getting a six-piece dissection of two squares into a different two squares by using two overlaid tilings, perhaps this image will help enlighten you. The two green squares can be dissected in six pieces into the two red squares; in each case, the larger of the two squares is split into five pieces (a square in its center surrounded by four congruent irregular quadrilaterals) and the smaller of the two squares is unsplit. —David Eppstein (talk) 23:54, 29 November 2012 (UTC)[reply]

What connection with the theorem?
The section title begins with "Pythagorean theorem"…
— Aughost (talk) 02:34, 30 November 2012 (UTC)[reply]

...and ends with "dissections". This is a dissection. The connection to the theorem is a different set of dissections, the 5-piece two-squares-to-one dissections. I think this one is relevant enough to mention in the article (at least at the single sentence length it currently is given) but may not deserve its own separate section. —David Eppstein (talk) 03:12, 30 November 2012 (UTC)[reply]

So you have to define a "dissection", with a source. With planar surfaces,
would you explain here what is a "dissection", please?
— Aughost (talk) 09:29, 30 November 2012 (UTC)[reply]

There is a source already given. It is an entire book about dissections. Additionally, the article gives a wikilink to a separate article with a definition. I have no idea what you mean by "with planar surfaces". —David Eppstein (talk) 13:47, 30 November 2012 (UTC)[reply]

It's also clear from the context (to me at least) what is meant by the term "dissection". Sławomir Biały (talk) 13:48, 30 November 2012 (UTC)[reply]

Puzzle

Easy to understand, without any doubt about a word like "dissection", two different assemblages of a same set of puzzle pieces have equal areas. It is a principle of proof of the Pythagorean theorem, badly exposed in the current section about the theorem, where we see only one shape formed by five pieces: a square, the size of which is denoted by c in the text. Here the image is better, with the two different shapes used to prove the theorem.
194.153.110.5 (talk) 13:27, 30 November 2012 (UTC)[reply]

It may be "badly expressed" in the current version, but those two versions shown in the current version are not original research, because they both appear in that form in the mathematical literature. I don't think the same thing can be said for your figure. Additionally, your figure is related to Perigal's dissection but does not show the much older one of Al-Nayrizi. —David Eppstein (talk) 13:51, 30 November 2012 (UTC)[reply]