![]() | Pythagorean tiling has been listed as one of the
Mathematics good articles under the
good article criteria. If you can improve it further,
please do so. If it no longer meets these criteria, you can
reassess it. Review: December 15, 2016. ( Reviewed version). |
![]() | 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:
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![]() | This article is rated GA-class on Wikipedia's
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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)
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)
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)
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)
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.
![]() of the grid in dashed red ![]() take the previous positions of a square in dashed red |
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. Here is the last sentence in section
"Pythagorean theorem and dissections": 194.153.110.5 ( talk) 14:20, 27 November 2012 (UTC) |
The Pythagorean theorem does not exclude the particular case where a right triangle is isosceles. The banner is
now removed, that suggested that the section about the theorem could be transported, not the whole article, into section "Proofs"of "Pythagorean theorem", because all proofs of the theorem through a tiling are still valid in case of isosceles right triangle ( a = b ), while the article says that a "Pythagorean tiling" is a tiling by squares of two different sizes ( a ≠ b ).
If we want to expose in this article a correct proof of the theorem through a tiling,
we have to modify the definition of a "Pythagorean tiling". The new definition would be:
a Pythagorean tiling is a tiling of the Euclidean plane by squares of equal or different sizes.
109.6.129.249 (
talk) 16:29, 1 December 2012 (UTC)
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)
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)
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)
No original research,
as said above. With these two positions of the grid in dashed red relative to the tiling, we get the same cuttings as on the
third image of this section.
194.153.110.5 (
talk) 14:29, 30 November 2012 (UTC)
A group of geometric transformations leaves unchanged the tiling and the grid. So the grid must be displayed in the first section of the article. The first image here shows four arrows, for a same transformation that preserves grid and tiling: a translation. However, in introduction of the article is defined a "Pythagorean tiling": a base of proofs of the theorem. And all copies of the original triangle are very visible in another image, where all hypotenuses are in dashed red. With that image without arrows, as first image with something about mathematics, we would respect chronological order of historical discoveries about such grids.
What image to illustrate the group of transformations, what do you think?
109.6.129.249 (
talk) 10:26, 1 December 2012 (UTC)
We see no grid in the current article, it will be necessary to show a grid, of course.
To avoid too numerous images, a same image will deal with several subjects, indeed.
On the image near the lead, I prefer
a grid that shows
periodic copies of the original triangle.
194.153.110.5 (
talk) 13:37, 1 December 2012 (UTC)
I am happy enough with the undecorated image that apperas first in the article. I think the fact that it is periodic is obvious. It might be possible to draw an image that illustrates both the translational and rotational symmetries of the tiling, but just superimposing another square grid on top of it won't do that. — David Eppstein ( talk) 16:02, 1 December 2012 (UTC)
I am not sure to understand. Anyway,
on 'Commons' everybody can search an image about our subject. Maybe someone will soon create a marvelous image…
109.6.129.249 (
talk) 16:44, 1 December 2012 (UTC)
GA toolbox |
---|
Reviewing |
Reviewer: Tessaract2 ( talk · contribs) 17:55, 13 December 2016 (UTC)
I am currently reviewing this or am not at the computer.Almost done! However, I need a second opinion on the copyvio report. Thanks
User:David Eppstein for the info! (See below.)
Tessaract2
Talk 17:55, 13 December 2016 (UTC)
A good article is—
Criteria | Notes | Result |
---|---|---|
(a) (prose) | Very concise, no grammar issues |
![]() |
(b) (MoS) | Seems to pas the Mos well enough. |
![]() |
Criteria | Notes | Result |
---|---|---|
(a) (major aspects) | Covers major aspects of the topic. |
![]() |
(b) (focused) | Does not go into too much detail from what I could tell. |
![]() |
Notes | Result |
---|---|
Meets NPOV, and not sure how it couldn't. |
![]() |
Notes | Result |
---|---|
Most edits made today are by the same user. |
![]() |
Result | Notes |
---|---|
![]() |
After followup on a talk page comment I made (see below) I can safely say this is a pass! |
Please add any related discussion here.
So the
copyvio detector has an over 75% confidence, but it seems like coincidencebasic info that is needed anyways for most of it. I need another opinion here.
Tessaract2
Talk 18:46, 13 December 2016 (UTC)
![]() | Pythagorean tiling has been listed as one of the
Mathematics good articles under the
good article criteria. If you can improve it further,
please do so. If it no longer meets these criteria, you can
reassess it. Review: December 15, 2016. ( Reviewed version). |
![]() | 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:
| ![]() |
![]() | This article is rated GA-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||
|
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)
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)
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)
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)
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.
![]() of the grid in dashed red ![]() take the previous positions of a square in dashed red |
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. Here is the last sentence in section
"Pythagorean theorem and dissections": 194.153.110.5 ( talk) 14:20, 27 November 2012 (UTC) |
The Pythagorean theorem does not exclude the particular case where a right triangle is isosceles. The banner is
now removed, that suggested that the section about the theorem could be transported, not the whole article, into section "Proofs"of "Pythagorean theorem", because all proofs of the theorem through a tiling are still valid in case of isosceles right triangle ( a = b ), while the article says that a "Pythagorean tiling" is a tiling by squares of two different sizes ( a ≠ b ).
If we want to expose in this article a correct proof of the theorem through a tiling,
we have to modify the definition of a "Pythagorean tiling". The new definition would be:
a Pythagorean tiling is a tiling of the Euclidean plane by squares of equal or different sizes.
109.6.129.249 (
talk) 16:29, 1 December 2012 (UTC)
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)
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)
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)
No original research,
as said above. With these two positions of the grid in dashed red relative to the tiling, we get the same cuttings as on the
third image of this section.
194.153.110.5 (
talk) 14:29, 30 November 2012 (UTC)
A group of geometric transformations leaves unchanged the tiling and the grid. So the grid must be displayed in the first section of the article. The first image here shows four arrows, for a same transformation that preserves grid and tiling: a translation. However, in introduction of the article is defined a "Pythagorean tiling": a base of proofs of the theorem. And all copies of the original triangle are very visible in another image, where all hypotenuses are in dashed red. With that image without arrows, as first image with something about mathematics, we would respect chronological order of historical discoveries about such grids.
What image to illustrate the group of transformations, what do you think?
109.6.129.249 (
talk) 10:26, 1 December 2012 (UTC)
We see no grid in the current article, it will be necessary to show a grid, of course.
To avoid too numerous images, a same image will deal with several subjects, indeed.
On the image near the lead, I prefer
a grid that shows
periodic copies of the original triangle.
194.153.110.5 (
talk) 13:37, 1 December 2012 (UTC)
I am happy enough with the undecorated image that apperas first in the article. I think the fact that it is periodic is obvious. It might be possible to draw an image that illustrates both the translational and rotational symmetries of the tiling, but just superimposing another square grid on top of it won't do that. — David Eppstein ( talk) 16:02, 1 December 2012 (UTC)
I am not sure to understand. Anyway,
on 'Commons' everybody can search an image about our subject. Maybe someone will soon create a marvelous image…
109.6.129.249 (
talk) 16:44, 1 December 2012 (UTC)
GA toolbox |
---|
Reviewing |
Reviewer: Tessaract2 ( talk · contribs) 17:55, 13 December 2016 (UTC)
I am currently reviewing this or am not at the computer.Almost done! However, I need a second opinion on the copyvio report. Thanks
User:David Eppstein for the info! (See below.)
Tessaract2
Talk 17:55, 13 December 2016 (UTC)
A good article is—
Criteria | Notes | Result |
---|---|---|
(a) (prose) | Very concise, no grammar issues |
![]() |
(b) (MoS) | Seems to pas the Mos well enough. |
![]() |
Criteria | Notes | Result |
---|---|---|
(a) (major aspects) | Covers major aspects of the topic. |
![]() |
(b) (focused) | Does not go into too much detail from what I could tell. |
![]() |
Notes | Result |
---|---|
Meets NPOV, and not sure how it couldn't. |
![]() |
Notes | Result |
---|---|
Most edits made today are by the same user. |
![]() |
Result | Notes |
---|---|
![]() |
After followup on a talk page comment I made (see below) I can safely say this is a pass! |
Please add any related discussion here.
So the
copyvio detector has an over 75% confidence, but it seems like coincidencebasic info that is needed anyways for most of it. I need another opinion here.
Tessaract2
Talk 18:46, 13 December 2016 (UTC)