Talk:Thales's theorem

Correct name?

Surely it should be Thales's theroem or Thales Theorem...? Jmccann: I agree.

Jmccann: I know the Greek letters don't look good, I'll spiff it up if someone else doesn't get to it first.

http://www.bartleby.com/141/strunk.html#1

I quote: Form the possessive singular of nouns with 's. But, later, Exceptions are the possessives of ancient proper names in -es and -is.

[[Jmccann: As a James, I am always bugged when someone refers to my stuff as James' (as if James is the plural of Jame). I left it as is because there seem to be several links to it. Basically, I am not excited enough to get worked up about it. My vote is for Thales's theorem. I had never heard of an exception for ancient proper names before this.

I think it is an exception for other words and names ending in "s" too, or at least it was. Eric Kvaalen (talk) 16:19, 24 January 2009 (UTC)

I think "Thales' Theorem" is correct. The spelling, not the theorem. Although that looks pretty correct, too. -- ESP 17:26 14 Jul 2003 (UTC)

When it comes to theorems of Greeks whose names end with an -s, there are usually three varations: Thales' theorem, Thales's theorem, and Theorem of Thales. All three are generally seen as acceptable. Other examples: Menelaus, Pappus of Alexandria. --Tokek 12:05, 27 Feb 2005 (UTC)

Quote "Since the sum of the angles of a triangle is equal to two right angles, we have

   2γ + γ ′ = 180°"

How would 2y + y be equal to two right angles? Dilbert 01:12, 2 April 2006 (UTC)

Thank You! This is very helpful. 72.197.201.129 01:13, 16 May 2006 (UTC)

Thales' other theorem

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)

The french page is very good !

Yes, there's an article: the intercept theorem. Eric Kvaalen (talk) 16:19, 24 January 2009 (UTC)

Sacrifice of a bull

I added this. SmokeyTheCat 14:40, 19 April 2007 (UTC)

More on Thales' other theoreme

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)

History

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).

Set of all right triangles in a semi circle

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)

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)

uses in trigonometry

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)

Euclid III proposition 31 or Euclid III proposition 33 ?

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)

Third Proof

The third proof doesn't look correct to me. The step 'Since lines AC and BD are parallel' doesn't seem justified by the process of mirroring the triangle, though perhaps I'm missing something. -- Wgsimon (talk) 11:12, 14 April 2015 (UTC)

It is a property of reflections. Note that reflection twice on lines being perpendicular to each other (think of the axis in a coordinate system for instance) is the same as a rotation by 180 degrees, which maps lines into parallel lines. However it might be helpful if the provided picture actually fully illustrates the reflection/mapping process which it currently does not. Also instead of reflecting twice on perpendicular lines one could simply use one reflection through the circle center.--Kmhkmh (talk) 12:21, 14 April 2015 (UTC)

Thales' theorem and reflections

P.S. I added a drawing hopefully illustrating the reflections a bit better. However it might be a good idea to rewrit and simplify the proof using one single point reflection through the circle center. In addition there should be some explicit mentioning of the proof using properties of reflection. Linking to Reflection (mathematics) would also be good idea, though that article might not be that helpful to many readers its current state. IF somebody goes for such arewrite he can use the picture one the right.--Kmhkmh (talk) 13:15, 14 April 2015 (UTC)

How about:

"Let $ABC$ be a triangle in a circle where $AB$ is a diameter in that circle. Then construct a new triangle $ABD$ by rotating triangle $ABC$ by 180° about the center of the circle. A rotation of 180° maps lines onto parallel lines. Since lines $AC$ and $BD$ are thus parallel, likewise for $AD$ and $CB$, the quadrilateral $ABCD$ is a parallelogram. Since lines $AB$ and $CD$ are both diameters of the circle and therefore are equal length, the parallelogram must be a rectangle. All angles in a rectangle are right angles."

-- Wgsimon (talk) 15:25, 14 April 2015 (UTC)

Can someone please fix the labelling of the accompanying diagram - it’s inconsistent with the labelling in the text for this proof and so totally unnecessarily confusing AstuteGrapefruit (talk) 10:55, 23 March 2018 (UTC)

How did Thales prove this?

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)

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)

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)

Alternate proof of the converse using geometry

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)

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)

cool spot

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)

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)