Talk:Thales's theorem

message: Many of the interwiki links describe a different theorem, also attributed to Thales, proving that parallel lines intersecting a pair of intersecting lines create similar triangles. (See :fr:Théorème de Thalès for probably the best explanation). What is this theorem called in English, and is there an article here about it? (There should be.) Rigadoun 20:49, 2 August 2006 (UTC)
replies: text: Yes, there's an article: the intercept theorem. Eric Kvaalen (talk) 16:19, 24 January 2009 (UTC)
thread_title: Thales' other theorem

message: I added this. SmokeyTheCat 14:40, 19 April 2007 (UTC)
thread_title:  Sacrifice of a bull 

message: Could someone please add information about Thales' other attributed theorem, which is often stated as "parallel lines intersecting a pair of intersecting lines create similar triangles," or "when parallel lines are intersected by two or more lines lines, the corresponding segments in the parallel lines are proportional."
In the French Wikipedia, this other theoreme is called Thales' Reciprocal Theoreme, and in the Spanish Wikipedia it's called Thales' FIRST theoreme. 
Thanks!
:I'm doin' it. Eric Kvaalen (talk) 16:19, 24 January 2009 (UTC)
thread_title:  More on Thales' other theoreme 

message: to pic a nit, you cant emperically discover a theorem. It isn't a theorem, by definition, until proven.
In any case, lots of geometric theroms are readily observed or intuitive, yet a challenge to prove, I'm not sure of the point of that statement.
132.3.33.68 (talk)  —Preceding undated comment added 20:13, 29 June 2011 (UTC)
thread_title:  History 

message: This may be intuitive, but I was wondering if all right triangles can be generated inside a semi-circle. At least all being congruent to one generated inside a semi-circle. The answer is naturally 'yes', with a little thought... and further some of the proofs would be incomplete if this was not true. So why dont we just state it somewhere in the article. Like: "All right angle triangles of a given hypotenuse can be generated in a semicircle of equal radius". Then I could just read it instead of thinking about it.  — Preceding unsigned comment added by 96.49.55.157 (talk) 02:26, 4 September 2012 (UTC)
replies: text: That fact is stated in the article, in the #Converse section: a right triangle's hypotenuse is a diameter of its circumcircle. —Bkell (talk) 04:03, 4 September 2012 (UTC)
thread_title:  Set of all right triangles in a semi circle 

message: i belive that it should be mencioned the use in trigonometry of this theorem since the right triangle incribed has a constant hypotenuse it acts as a unit circle for positive calculations of sine and cosine functions --half-moon bubba (talk) 19:51, 15 December 2012 (UTC)
thread_title:  uses in trigonometry 

message: The article refers to Euclid's elements Book III proposition 33 but as far as I know it is proposition 31 of the same book, can somebody check? (for the moment i changed it in the article, if somebody knows better please revert)
WillemienH (talk) 20:24, 19 September 2014 (UTC)
thread_title:  Euclid III proposition 31 or Euclid III proposition 33 ? 

message: There are three proofs offered, but all seem to rely on a number of other pieces of Euclidean geometry.  Since Thales is two centuries earlier, then he obviously couldn't have used Euclid's work.  So did all of Euclid's "work" predate Euclid?  Or is there some other proof that Thales had?
--David Garfield (talk) 17:12, 31 July 2016 (UTC)
replies: text: Well most if not almost all mathematical knowledge in the elements predates Euclid, Euclid primarily compiled and organized the mathematical knowledge of his time rather than discovering it. But i guess it is often hard to pinpoint for sure at what time a certain bit of mathematical knowledge was commonly known among scholars. Another thing is that discovery by or attribution of theorem to a person doesn't necessarily imply proof by that person either.--Kmhkmh (talk) 17:25, 31 July 2016 (UTC)
replies: text: I agree with everything written above and would add that there is no way to know exactly how Thales proved (if he did) this result since no written records still exist. The results on this page are all conjectures based on knowledge that Thales was likely to know or be able to work out himself. --Bill Cherowitzo  (talk) 17:39, 31 July 2016 (UTC)
thread_title:  How did Thales prove this? 

message: This proof doesn't seem correct. It starts out with an Circle that has the hypotheneuse AC as diameter and follows that the vertex B must be on the circle althought it was to supposed to show the converse.  — Preceding unsigned comment added by 2A02:908:1088:4580:34D9:BD4D:C66C:7204 (talk) 13:06, 21 January 2019 (UTC)
replies: text: One of several ways to state the converse is that the hypotenuse of a right triangle is a diameter of the circumscribed circle. In this proof, the hypotenuse of the right triangle is taken as the diameter of a circle and then it is shown that the third vertex of the triangle is on the circle, that is, the circle is the circumscribed circle of the right triangle, thus proving the converse. I see nothing wrong with the proof although I think it should have a reference. --Bill Cherowitzo  (talk) 21:48, 21 January 2019 (UTC)
thread_title:  Alternate proof of the converse using geometry 

message: In 'First proof', drop the perpendicular from B and the angle is also partitioned into alpha/beta.
Should I add this? Darcourse (talk) 10:02, 15 August 2023 (UTC)
replies: text: If it is not needed in the proof, then it's not really too helpful to add to a diagram or specifically call attention to, in my opinion. –jacobolus (t) 15:08, 15 August 2023 (UTC)
thread_title:  cool spot