Talk:Similarity (geometry)

message: I don't have explicit literature reference at hand right now, but I think it should be mentioned that similar triangles are (or rather provide) an important proof technique in elementary geometry.--Kmhkmh (talk) 14:01, 11 April 2018 (UTC)
replies: text: Added something. You may want more. --Bill Cherowitzo  (talk) 23:20, 11 April 2018 (UTC)
thread_title:  Similar triangles and proofs 

message: 1. If two angles are equiangular, then the ratio of the corresponding sides is same as the ratio of the corresponding medians.
2. If two angles are equiangular, then the ratio of the corresponding sides is same as the ratio of the corresponding angle bisector segments.
3. If two triangles are equi, then the ratio of corresponding sides is same as the ratio of the corresponding altitudes.
4. If one angle of a triangle is equal to one angle of another triangle and the bisectors of these equal angles divide the opposite side in the same ratio, then the triangles are similar.
5. If two sides and a median bisecting one of these sides of a triangle are respectively proportional to the two sides and the corresponding median of another triangle, then the triangles are similar.
6. If two sides and median bisecting the third side of a triangle are respectively proportional to the corresponding sides and the median of another triangle, then the two triangles are similar. Huzaifa abedeen (talk) 16:32, 18 February 2021 (UTC)
thread_title:  Some results based on the triangle similarly 

message: Can Lines (or line segments, or "sides" of a figure) be said to be "similar"?  Usually it seems the word "proportional" is just used.  But if curves (like parabolas) are described as being similar, it seems that all line segments must be similar.  The lead paragraph just uses the word "objects" as what similarity applies to, and later in the article it says it applies to "polygons", and "curves".  But what about lines (line segments, & "sides" of figures)?  Limitations of what the term properly applies to is not clear, but lines (segments) aren't mentioned in the lists/examples. DKEdwards (talk) 02:10, 16 November 2021 (UTC)
replies: text: I have added lines and line segments to . I have also clarified in the lead that congruent shapes are similar (this applies to lines but not to line segments). D.Lazard (talk) 10:17, 16 November 2021 (UTC)

text: (straight) lines and line segments on their ownare always similar (contrary to other curves), which is probably the reason it wasn't mentioned specifically as similarity in this case is automatically given and loses its distinguishing feature.--Kmhkmh (talk) 13:40, 16 November 2021 (UTC)
thread_title:  Lines?  

message: I propose to illustrate the current section titled “Ratios of sides, of areas, and of volumes” with the present image.   Arthur Baelde (talk) 13:47, 14 January 2022 (UTC)
replies: text: This triangle partition seems very specific to this triangle and this similitude ratio. So, instead of clarifying the concept, it may confuse non-mathematicians. I am against to add this image. D.Lazard (talk) 14:34, 14 January 2022 (UTC)
replies: text: What specificity?  We are not in considerations of the article “Square‑cube law”.  We have to say neophytes that a similarity is an object of pure mathematics.  Its coefficient cannot always be written as a scale in percent like displayed by a machine that prints onto papers.  Of course I thought of √2 among irrational square roots of integers.  But isosceles right triangles are all similar,  and anyone will know one fine day the story that multiplies an area of square by 2,  if interested in mathematics.  And then I thought of a triangular tiling that would be √3 times as large as each element of tiling:  a right triangle having a 60 degrees angle.  But if we are moving away from √2,  we might as well choose √5.  Notice I am not the inventor of this kind of tiling,  the article could include a link to “Pinwheel tiling”.   Arthur Baelde (talk) 10:42, 15 January 2022 (UTC)

text: You may prefer one equality only on the new image,  instead of three.  So here is on the right a possible version to insert in the article.   Arthur Baelde (talk) 14:24, 18 January 2022 (UTC)
replies: text: The first image in Pinwheel tiling is much clearer and much more aesthetic. It is thus more convenient for illustating the section on triangles. D.Lazard (talk) 15:24, 18 January 2022 (UTC)
replies: text: Here you are talking about the first section,so I repeat.  I propose to illustrate the fifth section titled “Ratios of sides, of areas, and of volumes”,   with one or the other image here presented.   Arthur Baelde (talk) 17:53, 18 January 2022 (UTC)
replies: text: The relationship of your image with this section is really unclear, and this makes the image unsuitable. Here, it is the square-cube law that deserves to be illustrated. A good choice would be an image of a Rubik's Cube, with the explanation that it is formed with 3^3=27 cubes, counting the non-visible interior cube. D.Lazard (talk) 18:47, 18 January 2022 (UTC)
replies: text: You look like someone who does not understand.  First I propose a square, not a cube.  Later perhaps we could include a more difficult three‑dimensional example.   Arthur Baelde (talk) 14:12, 19 January 2022 (UTC)
thread_title:  Example of coefficient on a new image