Talk:Geometric mean theorem

Suggestion for improvement of diagram

area of grey square = area of grey rectangle

I think the dashed curve between A and E should be erased. As far as I can see it plays no role in the derivation, and it looks like an attempt to run the circle through E whereas there is no claim that E is on the circle (and indeed it appears not to be). Duoduoduo (talk) 17:59, 28 May 2013 (UTC)[reply]

The purpose of the 2 dashed curves/partial circles is to illustrate the ruler and compass construction (application). In addition the dashed half circle encodes that the triangle has an right angle and the dashed quarter circle indicates line segments/quadrilateral sides of equal length. All that was also the reason, why the diagram was placed as the beginning of the article, as it serves as an illustration for 3 slightly different things: The general configuration/situation, the first proof and the ruler & compass construction. Otherwise we would have essentially same drawing (+/- dashed lines) several times, which I somewhat disliked for reason of aesthetics and (unnecessary) redundancy.--Kmhkmh (talk) 22:50, 28 May 2013 (UTC)[reply]

Several comments:

1. I don't think the text or caption is clear on what the AE arc is. Without even saying that D is the center of a circle containing arc AE, the picture does not convey the information that DA=DE. I think it would be better to get rid of the arc AE and just label DE with its length p.

2. I'm not sure why you reverted my moving the ruler and compass discussion away from the section on the theorem. The section labeled Theorem should simply contain the statement of the theorem (and its converse). The ruler and compass discussion is not the theorem.

3. I don't see how it helps to have the picture in the lede -- maybe you could clarify the caption to show that it is a restatement of what's in the text of the lede. Duoduoduo (talk) 23:26, 28 May 2013 (UTC)[reply]

Regarding 1.): Imho it rather clear from drawing that the dashed lines are partial circles (circles are relatively easy to recognize and distinguish from other curves), hence I don't really see much of a problem there. Moreover it becomes clear either way as soon as one reads the ruler & compass construction paragraph. Labeling the 2 sides with p is an alternative to indicate equal lengths, but it still doesn't quite illustrate the use of the compass.

Regarding 2.): Because your separation, destroyed the context of the first sentence of that paragraph referring to the line before (not existing anymore if you move the paragraph to a different) chapter. Of course that could be fixed by changing the lead sentence as well. However to me it makes little sense to drag that relatively small amount of content over several chapters. It all fits perfectly into one. If you think the title theorem for that section is inappropriate or too "misleading" it can be changed/augmented.

Regarding 3.) The reason for it being in the lead is because it illustrates several things, the lead, the theorem, the similarity proof and the ruler and compass & construction. Hence it makes sense to show it already in the lead. However showing at the beginning of theorem chapter (sort of in the middle) might work equally well, in particular since the description as an equality of areas is not given in the lead explicitly.--Kmhkmh (talk) 00:51, 29 May 2013 (UTC)[reply]

Pythagoras theorem

In a right angled triangle the suare of the hypotension is equal to the sum of the square of remaining two sides @[[User:Tushar Dolui 103.145.18.85 (talk) 14:32, 24 June 2023 (UTC)[reply]