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Pythagoras's theorem similar triangles proof.

[edit]

Voting period is over. Please don't add any new votes. Voting period ends on 19 Apr 2012 at 05:16:05 (UTC)

Original – Proof using similar triangles.
Reason
High technical standard and resolution, public domain, verifiable in article, complete file description. It adds value to article. It is a graphic so criteria 8 doesn't apply. I can't say anything about criteria 3.
Articles in which this image appears
Pythagorean theorem
FP category for this image
Wikipedia:Featured pictures/Diagrams, drawings, and maps/Diagrams
Creator
Gauravjuvekar
  • Support as nominator --Gauravjuvekar (talk) 05:16, 10 April 2012 (UTC)[reply]
  • Comment: something a bit different. I'd really like to see some reference to some book where this diagram is taken from, preferably with accompanying proof as laid out there: including the proof itself feels a bit OR, as if we're expected to validate it ourselves. Grandiose (me, talk, contribs) 10:30, 10 April 2012 (UTC)[reply]
    • Comment:I vectorized it from its bitmap version but I did find a book (textbook).:Geometry Standard X (textbook) Maharashtra State Board of Secondary & Higher Secondary Education Pune -411 004 (First Edition:2011) Page 23.

The figure there is at best described as "crude" with a simple right angled triangle ABC(B is the right angle) and a perpendicular BD onto AC(hypotenuse). The figure there is black and white with only the right angles marked(no other markings except vertices). The exact proof there is:
In \tri ABC, seg BD \perp hypotenuse AC ...(construction)


\ther \tri ABC ~ \tri ADB ...(similarity in right angled triangles)


\ther AB/AD=AC/AB ...(corresponding sides of similar triangles)


\ther AB^2=AC X AD ...(i)


Similarly, we have \tri ABC ~ \tri BDC


\ther BC/DC=AC/BC ...(corresponding sides of similar triangles)


\ther BC^2=AC X DC ...(ii)


\ther AB^2 + BC^2 =AC X AD + AC X DC ...[by adding (i) and (ii)]


=AC(AD+DC)


=AC X AC ...(A-D-C)


=AC^2


\ther AB^2 + BC^2=AC^2



I couldn't be bothered to use the math tags again so \tri means the triangle symbol(Delta), \ther means the therefore symbol(three dots) and X means the multiplication sign. Everything after ... are reasons for the corresponding statements.

I didn't originally reference it as the book is unreliable (IMO) with frequent errors. (eg:An image from Wikipedia is cited as htpp[sic]://en.wikipedia.org/wiki/pythagorean-themorem[sic] (pages 3, 4 and 5)[since when do Wikipedia articles have pages])I have several other reasons that don't belong here.


BTW I didn't understand what you meant by as if we're expected to validate it ourselves.--Gauravjuvekar (talk) 11:52, 10 April 2012 (UTC)[reply]

If you have a book which demonstrates that this image is correct and uses the proof - and is a reliable source - then add it. I would like to see one before I can support. Grandiose (me, talk, contribs) 18:50, 10 April 2012 (UTC)[reply]
  • Comment' -- I think this nomination is in the wrong forum. Here we assess the encyclopaedic value of pictures in articles, not mathematical proofs. And I can't see anything remarkable in this image. (BTW, the proof above makes little sense, there is no vertex D) -- Alvesgaspar (talk) 18:44, 10 April 2012 (UTC)[reply]
I believe the nomination is correct. The image significantly adds to the article by illustrating the proof. The proof given is in response to my verifiability/sourcing comment, not part of the nomination. Grandiose (me, talk,contribs) 18:50, 10 April 2012 (UTC)[reply]
@Alvesgaspar--The proof is not with regard to this figure, it's according to the one given in the book. For it to make sense, just switch labels of vertex C and B and rename H as D--Gauravjuvekar (talk) 03:55, 11 April 2012 (UTC)[reply]
  • Strong oppose -- Nothing extraordinary here. It is not even a good illustration of the proof in the article, which only refers to the lengths of the sides in the form: a, b, c, etc. Considerable sophistication is needed, in my opinion, for an illustration to win the star. Please browse the relevant part of our FP gallery to see what I mean. -- Alvesgaspar (talk) 19:12, 10 April 2012 (UTC)[reply]
    • Comment-I'm sorry but this is Wikipedia's FPC. FPs on Commons require a WOW factor. FPs on Wikipedia require encyclopedic value. So there need not be any thing extraordinary, just something very much educationally and encyclopedic-ally illustrative. Also, AC=b, BC=a, AH=d, BH=e, AB=AH+BH=d+e=c. It's one and the same thing.--Gauravjuvekar (talk) 04:01, 11 April 2012 (UTC)[reply]
  • Comment:I don't know how to add the reference so I added it to the source field on the file description page. Please correct it if it's wrong--Gauravjuvekar (talk) 04:14, 11 April 2012 (UTC)[reply]
Support: does everything that is required of it that I can see under the criteria, being clear, informative and adding considerably to understanding the proof, which would frankly be unintelligible to most readers without. Now verifiable. Grandiose (me, talk, contribs) 06:50, 11 April 2012 (UTC)[reply]
  • Support Very helpful, informative and enyclopedic.--GoPTCN 09:29, 11 April 2012 (UTC)[reply]
  • Oppose as is Firstly, don't mix the notational conventions. Use a,b,c,d,... or AB,AC,BC,... to denote edges, not both. Secondly, make it clear if the textbook is a source for the proof or the images or both. If it isn't both then I'd prefer to see the proof referenced too. Thirdly, we use arrows around the "c", but not other letters, be consistent. Any proof on the image description page should match the image. Finally, it doesn't really fit the article text perfectly. JJ Harrison (talk) 22:47, 11 April 2012 (UTC)[reply]
    • Comment:The capital letters are used to denote triangles and angles. The small are used to denote individual segments for simplicity. The article mainly uses small letters for denoting the sides in the proof. The textbook uses capital letters(AB) to denote angles, triangles as well as sides. The proof in Wikipedia article uses capital as well as small letters so both notations should be in the image(unless we change the proof in the article). On the image description page, I used only one form of notation(capital letters). If we replace the lowercase notations in the article with two uppercase notation form, we could do away with the smaller notations in the image;even the 'c', the arrows denoting length AB and the lines extended from A and B.

Yes, the textbook is a source for the figure and the proof.(The figure is slightly different, the positions of B and C are switched and H is labeled D but that doesn't really matter much) I didn't understand what you meant by we use arrows around the "c", but not other letters. The arrows around c denote the length of c is AB.(Just as AC is b and BC is a, AB is c). Writing it without the arrows in the same line as d and e would be confusing. Lastly, I really don't know how to make it fit the article text. Could you please explain the part about the 'c' and the arrows around it in detail?--Gauravjuvekar (talk) 04:02, 12 April 2012 (UTC)[reply]

  • I don't understand "doesn't even illustrate well the proof in the article": it illustrates Pythagorean_theorem#Proof_using_similar_triangles very well in my opinion, and some sort of diagram there is vital to the reader. I get JJ's points but they appear to be in a useful discussion about them.
FPCR #1 requires a high technical standard, something widely assumed to not really apply to SVGs, and I don't see that any part of it is an issue here. #2 requires a high resolution, not applicable to an SVG. #3: "Is among Wikipedia's best work." ~ I don't think there's a better way of presenting this, if JJ's points are addressed. Otherwise #3 is appropriately covered by what I believe to be "diagrams and other illustrations are clear and informative." and "highly informative". #4 is clearly fulfilled, and I beleive as regards #5 that it is vital to a reader understanding the proof being given, unless they're very good at picturing it in their heads. Verifiability I believe is there, subject to any of JJ's concerns being fulfilled. Which criterion do you believe is not fulfilled? I'd hardly describe my approach as "more or less hollow". Grandiose (me, talk, contribs) 10:16, 14 April 2012 (UTC)[reply]
  • Comment -- Let me clarify my previous comments. First, the drawing does not illustrate well the proof in the article because it contains excessive and superfluous information. As already stated, more than once, the only features that need to be labelled are the edges. Second, the encyclopaedic value of an illustration doesn't quality if automatically as a FP. If it were so, most illustrations in the articles would be featured. The bottom line is: a picture, any picture, must be exceptional in some way to win the star. Which is not obviously the case. Alvesgaspar (talk) 12:04, 14 April 2012 (UTC)[reply]
Could you please clarify which of the criteria requires a given picture to be "exceptional"? #3 is the closest but draws a comparison between the image and similar images, where this would do well. Grandiose (me, talk, contribs) 12:32, 14 April 2012 (UTC)[reply]
  • From the top of the FPC page: Featured pictures are images that add significantly to articles, either by illustrating article content particularly well, or being eye-catching to the point where users will want to read its accompanying article. Taking the adage that "a picture is worth a thousand words," the images featured on Wikipedia:Featured pictures should illustrate a Wikipedia article in such a way as to add significantly to that article, according to the featured picture criteria. -- Alvesgaspar (talk) 12:44, 14 April 2012 (UTC)[reply]
  • Please read the entire section in the article, it won't take long. The second paragraph uses the vertices to denote triangles. Hence they are needed(A, B, C and H). But it refers to the hypotenuse as "c" being divided into "d" and "e" at point "H" and the ratios below use the a, b, c, d, e forms(in math tags). Hence both forms are needed. Change the wording in the article and I will change/remove the markings in the image accordingly. I feel that you are confusing Commons and Wikipedia FPC. Commons FP require WOW factor so this image is unlikely to pass at Commons because it's "too simple". Wikipedia FPCs require EV which I feel is satisfied by this image and hence, this nomination is at Wikipedia.--Gauravjuvekar (talk) 15:04, 14 April 2012 (UTC)[reply]
  • Oppose I think the image helps understanding the accompanying text in the section. I also understand c has an arrow and not d and e, but since author chose to use color on d and e, maybe it's redundant to use arrow on c. Maybe section could be rewritten to use notation AB, BC, CD instead of a, b, .... this would make a, b, c, ... useless and unclutter the diagram a bit. This also somehow meets JJ Harrison suggestion. I oppose for lack of consistency, but mostly because author used sans serif fonts. I've always seen serif fonts used in mathematics diagrams. - Blieusong (talk) 22:51, 14 April 2012 (UTC)[reply]
    • Comment:Wikipedia:Manual_of_Style/Mathematics#Graphs_and_diagrams doesn't give a consistent guideline. It says that matching the font with the text used in the article is better. The article uses plain text as well as LaTeX. LaTeX currently uses serif fonts in italics but I don't know which font it exactly is. I could change it in the file if I know what font LaTeX rendering uses. Please give the font and I will change it accordingly (Please state whether the file should be overwritten or a new file used).Problem is that the plain text uses sans serif while LaTeX uses serif font.
I don't think just the colour on 'c' would suffice as floating the 'c' wouldn't be much effective. I think the arrow is very much needed.--Gauravjuvekar (talk) 11:38, 15 April 2012 (UTC)[reply]
  • Wiki (and most web pages) displays sans serif fonts for readability reasons only (might change with new high density pixels screens), but you are probably right when you mention the font should match the article's. Unfortunately for you the article has mix of both, since the formulas are rasterized from a typical LaTeX output. I would stuck to the serif version, but now it's only a matter of tastes. My "inconsistency" and "removing useless elements points" still stand. - Blieusong (talk) 18:49, 17 April 2012 (UTC)[reply]
  • LaTeX uses Computer Modern font (it's actually a family of font, and a default setup LaTeX uses the roman italic variant of it for mathematical formulas). It's free to use, and I think it's be easy to find version (true type?) you can use from your vector program (Inkscape it seems). This would make your diagram more consistent with the formulas for sure. - Blieusong (talk) 18:55, 17 April 2012 (UTC)[reply]
  • Oppose It is indeed of reasonable technical quality and adds value to understanding one part of the article. However, it is dubious whether it is one of Wikipedia's best works. It certainly does not outshine the myriad other pictures on Wikipedia describing various different proofs of the Pythagorean theorem. For example this proof by rearrangement of parts is a well-executed vector illustration of a quite different proof which is not any less beautiful, but it is nonetheless not a Featured Picture. Furthermore, this picture does not stand on its own - it seems more an accessory to the accompanying proof rather than a clear visual demonstration of the said proof. As a side note, I agree with Blieusong regarding the inconsistency wherein the image description refers to the line segments by their vertex endpoints whereas the article uses the labelled edges. Purpy Pupple (talk) 23:16, 17 April 2012 (UTC)[reply]
  • Oppose per JJH, Alvesgaspar, and Purpy Pupple. Clegs (engage in rational discourse) 07:54, 18 April 2012 (UTC)[reply]

Not Promoted --Makeemlighter (talk) 21:57, 19 April 2012 (UTC)[reply]

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