Talk:Intercept theorem

Error in calculating the pyramid's height?

The article says:

$C=2m+63m+{\frac {230m}{2}}=180m$

But why is the addition of "2m" needed? It seems an error. —Preceding unsigned comment added by 93.172.84.58 (talk) 07:34, 24 August 2009 (UTC)

You are correct, the 2m are actually included in the 63m shadow of the pyramid. I'll fix it.--Kmhkmh (talk) 08:09, 24 August 2009 (UTC)

Thanks. One more thing: I think "shadow of the pole (A)" should be changed to "shadow of the pole (B)".

About calculating the pyramid's height

It might be worth explaining that the two triangles (the pyramid's and the pole's) are similar only because the sun is very far and is thus practically "at inifinity". This makes the angle at the top of the triangles congruent. The picture is misleading because it shows the sun very low and thus it's not clear why the hypotenuse of the pole's triangle has the same slope as that of the pyramid's triganle. —Preceding unsigned comment added by 93.173.110.65 (talk) 01:11, 26 August 2009 (UTC)

Proof

Is it only me or the proof given in the article is way too complicated? I suggest this one:

That's exactly what the proof does, that picture is just a rotated version of the one in the proof.--Kmhkmh (talk) 15:36, 18 February 2011 (UTC)

Haha, sorry, I didn't know that notation of $|\triangle CDA|=|\triangle CBA|$, so I stopped reading the proof and did not pay attention on the figure. Then I went searching for another proof, my mistake, hehe. Thanks for the attention.

What is claim 4?

It says "Claim 4 can be shown by applying the intercept theorem for two lines." But what can be shown? What is claim 4? — Preceding unsigned comment added by 27.255.243.2 (talk) 09:52, 15 July 2015 (UTC)

claim 4 is stated in the formulation section.--Kmhkmh (talk) 01:41, 1 October 2015 (UTC)

temporary removal

I temporarly removed the following section, because for one it was unsourced but more importantly it lacks a proper explanation of the complex construction and its goal. I assume this is meant as a practical example for role the intercept theorem plays for the set of constructable numbers (explained further up in the article). However it might be be better choice to to construct a simpler 2 digits number to illustrate mechanics rather than going for a pi approximation. But in any to make such a picture a useful addition to the article, it requires some more detailed explanatory description.--Kmhkmh (talk) 01:39, 1 October 2015 (UTC)

The construction of a decimal number

A practical example of the intercept theorem in combination with number line. (Situation following revision October 15, 2015)

View

Animation

literature & links

• https://books.google.de/books?id=DnKLkOb_YfIC&pg=PA65
• http://www.walter-fendt.de/html5/men/intercepttheorem_en.htm
• http://planetmath.org/intercepttheorem
• https://books.google.de/books?id=FYmJDAAAQBAJ&pg=PA80
• https://www.geogebra.org/m/sH6TnqEU
• https://www.youtube.com/watch?v=82ZWcUrgnwU
• https://books.google.de/books?id=5L6BBwAAQBAJ&pg=PA135&

• https://www.youtube.com/watch?v=cACn06wXkYY

Thales' or Thales's

@Wcherowi: the other article is titled Thales's theorem, and there's also MOS:POSS. wumbolo ^^^ 21:40, 20 January 2019 (UTC)

Well to my knowledge both versions are correct and somewhat common in English. However if WP has a generally accepted house rule like MOS:POSS, that favours one version the case seems clear. Personally however I gave up on following the current state of the extensive manual of style (or caring much about it).--Kmhkmh (talk) 22:02, 20 January 2019 (UTC)

Wumbolo We just been through a long discussion at Stokes' theorem concerning the recent change to MOS:POSS and my reading of the result favored revisiting that change. I would suggest not making a change in the use of 's until that has been worked out. --Bill Cherowitzo (talk) 22:07, 20 January 2019 (UTC)

Out of curiousity. Do you have a link to the ongoing dispute/recent change with regard to s' vs s's issue--Kmhkmh (talk) 22:54, 20 January 2019 (UTC)

No I don't. The final consensus at Talk:Stokes' theorem was to not move the title (that is, not apply the current MOS:POSS) and carried a recommendation to review MOS:POSS. This decision was also placed on the bottom of the MOS talk page, but I haven't seen any further discussion yet. --Bill Cherowitzo (talk) 05:20, 21 January 2019 (UTC)

side splitter theorem

Also known as side splitter theorem Huzaifa abedeen (talk) 13:52, 18 February 2021 (UTC)

Intercept theorem or Basic proportionality theorem

I think there is a misconception in the entire article about Intercept theorem. As far as I know Intercept theorem states that "If three or more parallel lines make equal intercepts on a given transversal, they will make equal intercepts on any other transversal."

Whereas Basic proportionality theorem (BPT) states that "If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the sides in the same ratio". In fact the Basic proportionality theorem can be used to prove Intercept theorem itself. Please suggest your opinion whether to move the article to BPT or not. Nishānt Omm (talk) 13:40, 2 May 2022 (UTC)

No, first of all the theorem as original stated is called intercept theorem (as can be seen among others in the sources used in the article). The figure with three or more parallel lines is just variation of essentially the same statement und hence usually the same name is used for it.-Kmhkmh (talk) 19:15, 24 May 2022 (UTC)

proof of claim 1: angles

Angles SCB and SDA cannot be equal, the first is greater than 90 degrees, the second is less than 90 degrees. Unless the labels are wrong? 138.229.234.64 (talk) 19:54, 30 January 2023 (UTC)

Those are not angles but triangle areas. See the comment on the notation on top of the proof and note the difference between $\triangle$ (triangle) and $\angle$ (angle).--Kmhkmh (talk) 15:25, 1 February 2023 (UTC)

Converse of the second statement

I don't understand this part:

> However, the converse of the second statement is not true.

With the given configuration, if the second statement is true, i.e. if ${\frac {|SA|}{|SB|}}={\frac {|SC|}{|SD|}}={\frac {|AC|}{|BD|}}$, then the two formed triangles have the same ratio of corresponding sides and therefore are similar. I think it's obvious that bases of two similar triangles that share the same vertex are parallel. Isn't it? A counterexample might help. 5.232.53.5 (talk) 06:25, 6 July 2023 (UTC)

${\tfrac {|SA|}{|SB|}}={\tfrac {|AC|}{|BD|}}$ does not imply $AC\parallel BD$

In your case the (specific) converse is actually true, but that is because you formulated the condition in such a way that, that the equation of the first statement is included as well (${\tfrac {|SA|}{|SB|}}={\tfrac {|SC|}{|SD|}}$) and since for the first statement the converse is true it, it is true in your setting as well. However if you only start with the condition ${\tfrac {|SA|}{|SB|}}={\tfrac {|AC|}{|BD|}}$, so that equation of the 1st statement doesn't hold automatically as well then you can construct a counterexample (see graphic).--Kmhkmh (talk) 11:21, 21 September 2023 (UTC)

P.S.: Since this is an encyclopedic article rather than a textbook description not every result/detail needs to be (and often should not) explained as its purpose is more summary/survey of results and their connections. However I included the counterexamples now in a way that does not bloat the article or impairs readability of the article.--Kmhkmh (talk) 12:54, 21 September 2023 (UTC)

Thanks for the explicit counterexample. I hope you don't mind that I took the <math> tags out of your captions. Their output is prettier than using the {{math}} template, but unfortunately doesn't render properly when an image is clicked to make it render as a full-window modal view, so it's best to avoid them if possible. –jacobolus (t) 20:34, 21 September 2023 (UTC)

Well personally i hate (to use) the non-math tag options as they don't work across other language Wwikipedias and you have to bother with additional templates and special characters making it imho less editor friendly (as opposed to standard latex approach). However if somebody wants to use use them or switch to them for (current) display reasons, I have no real objections.--Kmhkmh (talk) 00:39, 22 September 2023 (UTC)

P.S. I don't quite the rendering issue with clicking on the image. When i click on on an image, then i get the image only without the text, that is nothing gets rendered anyway. What am I missing here? Is that a setting/preferences issue? Or related to the visual editor?--Kmhkmh (talk) 00:39, 22 September 2023 (UTC)

If you click e.g. the image in this current talk page section, the caption printed at the bottom of the modal image view is just "does not imply" – the <math> tags do not render at all. At least in a desktop browser; I'm not sure what happens on the mobile page. –jacobolus (t) 04:28, 22 September 2023 (UTC)