File talk:Euler diagram of quadrilateral types.svg

Marking logically empty regions

I'd like to suggest shading in the regions that are "empty"... e.g. since there are no rectangles that aren't either square or oblong, the regions within the rectangle but outside the square and oblong should be shaded. Spheniscine (talk) 13:53, 10 June 2013 (UTC)

Interesting idea. Logically, it makes sense, but it would add another graphical element, and thereby trade off clarity for logic. Coincidentally, my suggestion below provides the same information, albeit less explicitly. — Sebastian 07:10, 27 April 2015 (UTC)

Please see below... cmɢʟee⎆τaʟκ 23:14, 9 May 2015 (UTC)

Use dashed lines to convey information

Does the distinction between dashed lines convey any information, or was it just taken to reduce the amount of colors necessary? If the latter, then I suggest to use it to convey the information that a given shape is represented by a shape that already has a more specific name. (Since the diagram is designed to avoid that situation, this means that there is no shape available other than the ones already defined inside the given shape, or in the words of User:Spheniscine above, that the region between the given shape and the shapes it contains is empty.) This is already the case for the name "Rectangle", which is represented by a dashed Oblong, and the "Parallelogram", which is represented by a dashed Rhomboid. I'm therefore suggesting to change the following:

• Change to dashed: The "Simple quadrilateral" (which is represented by a Convex quadrilateral);
• Change to solid: The Convex quadrilateral (which contains shapes that are neither Dart nor Trapezium) and the Dart (which is the most general shape of a dart).

We could also consider using the same or similar colors for the dashed shapes and the specific shapes that have been used to represent them. E.g. the Rectangle and the Oblong could both use shades of red, and the square blue. — Sebastian 07:10, 27 April 2015 (UTC)

Proposed changes

That's a brilliant idea, Sebastian. I used dashed lines merely to let readers more easily track multiple parallel lines, but yours adds extra meaning while retaining that functionality. I've modified the diagram as on the right. Could you please write a succinct description of the meaning of the dashed lines for the caption, since I can't think of a good way to describe them? cmɢʟee⎆τaʟκ 23:27, 9 May 2015 (UTC)

P.S. Sorry I don't understand your last paragraph: as both squares and oblongs are rectangles, why should the oblong and rectangle be similar in colour but not the square?

I don't think we need add to the caption why a shape is dashed. It's not at all necessary to understand the picture and would distract the reader with things they never even wanted to know, as evidenced by the fact that nobody has asked about the existing dashes until now. Crazy people like you and me who voluntarily spend their free time on this can just read this talk page, or they will, as I did, enjoy discovering such things by themselves. I wouldn't want to spoil that fun. But since you're asking, and since this is connected with the coloring idea, here's my attempt at a description: (I'm using "we" to clearly distinguish our choices from mathematical facts. Similarly, I use capital letters for our shapes.)

We used dashed lines when there is a more exact name for the same shape. For example, we drew the Rectangle with a dashed line because the shape we chose can be more precisely called an oblong. To make it easy to see that our representation is an oblong and not a square, we gave the Rectangle representation the same color as our Oblong representation. — Sebastian 18:07, 10 May 2015 (UTC)

Thanks, Sebastian. You're quite right that it just complicates the caption, so let's leave it as is. Re more-exact names, I see what you mean now and am neutral about it. As long as the colours are easily distinguishable, please feel free to edit the "discussion" SVG image with a text editor (it should be pretty obvious what goes where). cmɢʟee⎆τaʟκ 23:12, 10 May 2015 (UTC)

I took the liberty to change your link above to display my changes. To be honest, I do see a disadvantage of it now: Names bordering a shape with the same color, such as "Rectangle" next to our Oblong can easily be taken to label the wrong shape. Since you're already not excited about the chance to reduce the number of colors, it may not be worth it after all. — Sebastian 18:56, 11 May 2015 (UTC)

Good example for combining two different kinds of information

I feel this is a very elegant diagram, which manages to combine both the logical relations as well as depicting the actual shapes. — Sebastian 07:10, 27 April 2015 (UTC)

Thanks, Sebastian. In case you're interested, there's also File:Euler_diagram_of_triangle_types.svg. cmɢʟee⎆τaʟκ 23:29, 9 May 2015 (UTC)

The Trapezium is too similar to the Parallelogram

The Trapezium looks almost like a Parallelogram. If one dragged out the rightmost corner, the angle between the left sides of these two shapes would become bigger, making the distinction clearer. — Sebastian 07:10, 27 April 2015 (UTC)

My personal opinion is that it's clear enough from the top-left corner which is intentionally dragged out away from the parallelogram it encloses. Dragging out the top-right corner would make the diagram a little untidier as the line segments on the right will no longer be parallel. cmɢʟee⎆τaʟκ 23:34, 9 May 2015 (UTC)

That's a misunderstanding; my suggestion doesn't lose any parallels. But I grant you that it will probably break something else you care about that I'm not aware of. Things like this are always a trade off. Where to draw the compromise for this picture will be ultimately your call.

I would like to explain what I had in mind, but I realize it's hard in words. Can we use mathematical notation for this? Should we label the corners A,B,C,D, beginning lower left clockwise? Which letter would you give each shape? How about this:

• Q = Simple quadrilateral
  • V = Concave q.
    • U = Dart (using "U" for the shape, avoiding "D" since it's used for the fourth corner.)
  • X = Convex q.
    • K = Kite
    • T = Trapezium
      • P = Parallelogram
        • H = Rhomboid
        • R = Rhombus
        • E = Rectangle
          • O = Oblong
          • S = Square

— Sebastian 18:07, 10 May 2015 (UTC)

To be honest, I'm not so keen on the idea of labelling corners:

1. Due to the spacing of the lines, the corners are no longer discernible points so it's unclear which vertices belong to which corners.
2. It will look even less like an Euler diagram (considering I've already overloaded it quite a bit).
3. It will be more cluttered, without much gain in understanding. — cmglee — continues after insertion below

Oh, sorry, another misunderstanding! I didn't mean to label the diagram. I just meant for us here to agree on a convention, so we can discuss this easier. — Sebastian 18:02, 11 May 2015 (UTC)

By the way, when you're satisfied, let me know and I'll port the changes back to the original. Cheers, cmɢʟee⎆τaʟκ 23:20, 10 May 2015 (UTC)

The picture is definitely an improvement already, so I have no objection to porting. But back to the topic of this section: I just changed it to "The Trapezium is too similar to the Parallelogram" to express the problem I'm trying to solve, while my original title just advocated one possible solution. I think the source of the problem is that the lower left angle of each of these are too similar. If α denotes the angle DAB per my above nomenclature, then this can be restated as α_T ≅ α_P. The distinguishing angle |α_T - α_P| = 63°-55° = 8° is smaller than any other distinguishing angle. (|α_S-α_X| = 72°-63° = 9° is about the same, but this is not what I'd call distinguishing, since the difference doesn't carry any information that would distinguish the types of quadrilaterals.) — Sebastian 18:02, 11 May 2015 (UTC)

On second look, I realize that the angle distinguishing the Kite from the Convex quadrilateral, is |α_K - α_X| = 72°-63° = 9°, too. That means that my original idea of moving all right corners C_S, C_X, C_T, C_P, and C_K becomes messy if we don't want to affect that angle. One could of course keep C_K and just move the other four C corners, but you may find that less elegant. — Sebastian 18:37, 11 May 2015 (UTC)

The chart is wrong

It falsely implies that oblongs are not rhomboids.  allixpeeke (talk) 19:43, 2 November 2016 (UTC)

allixpeeke, our article Rhomboid says “A parallelogram with right angled corners is a rectangle but not a rhomboid.”, which matches my understanding, but has no source. If you have a source, then you can add what the source says (along with a reference) to the article Rhomboid. If you don't have a reliable source but still believe not including rectangles is wrong, then I recommend discussing that at Talk:Rhomboid, and asking for sources. ◅ Sebastian 14:30, 30 November 2020 (UTC)