Talk:Kite (geometry)

Untitled
regarding the latest change, which is the former and which is the latter, it is unclear as you only mention kite flying in the sentence. Can you change it to "the geometric kite was inspired by the shape of the flying object" or whichever - I can't figureout which way it is. Onco_p53 11:09, 26 July 2005 (UTC)

The article is unclear regarding if the kite can be concave or only convex. In Hungary "deltoids" also include concave quadrilaterals having two pairs of equal sides, but of course concave deltoids can't be tangential. Cheers, SyP 20:46, 25 March 2006 (UTC)


 * In the USA we call non-convex deltoids "darts." I'm going to see if there's a Wikipedia page for them.... RobertAustin 16:06, 20 November 2006 (UTC)


 * Can we redirect "Deltoid" to "Kite" after dembuguity because it is also a Muscle?.--Dagofloreswi (talk) 00:03, 18 February 2009 (UTC)


 * Deltoid is currently a disambiguation page pointing to both the muscle and the shape, as well as to a few other meanings. I don't think we should change that. —David Eppstein (talk) 00:13, 18 February 2009 (UTC)


 * I have always defined "kite" to be convex, excluding the deltoid, dart, or arrowhead. Does anyone actually use the term "concave kite"?  Should we modify the definition?    D b f i r s   08:31, 25 April 2009 (UTC)

right kite
Is there such a thing as a right kite? I mean, a right triangle reflected over its hypotenuse? What properties does it have?
 * A right kite is a cyclic quadrilateral.&mdash;GraemeMcRaetalk 19:49, 24 June 2009 (UTC)

Quadrilateral Classification
I want to apologize for some changes I made earlier without consulting this discussion thread. I appreciate the author's respect and interpretation of these changes. The changes I suggested drive toward a general confusion that exists in geometry, albeit mainly at the high school level. Confusion arises when students attempt to classify quadrilaterls using specific properties to create a hierarchical relationship.

Let me give one such example. If we decide to classify quadrilaterals based on the the parallelism of sides, we end up with three major categories: Kites (no parallel sides), Trapezoids (1 set of parallel sides) and Parallelograms (2 sets of parallel sides.) I teach geometry at the high school level and this is the text's preferred classification. Following these rules, the rhombus and rectangle are special parallelograms and the square is a combination of the two.

The confusion arises when a statement, like the one I edited in this article, reads (to the effect): "any quadrilateral with an axis of symmetry must be either a kite or isosceles trapezoid." Such a statement makes the assumption that the reader is familiar with the classification method being used. It assumes the reader will conclude that rectangles, rhombi and squares can also be considered special Kites and Isosceles Trapezoids. If a student is using the classification method mentioned previously, confusion will occur.

Do the authors of this article feel it would be worth while to briefly describe the classification method used in the article and the subsequent, hierachical relationships? I understand the "correctness" of the article in its current state but wish to clarify some of the assumptions that are made.

Andrewbressette (talk) 19:26, 16 December 2009 (UTC)


 * The Quadrilateral article has a taxonomy of quadrilaterals. All references to classification should be made in accordance with that hierarchy.&mdash;GraemeMcRaetalk 22:40, 16 December 2009 (UTC)

I did not realize that this issue has been brought up before. "Is a rhombus a kite?" Here, at Wikipedia, the consensus seems to be yes, but in US high school geometry, the answer is no. The quadrilateral classification chart (Euler diagram) on the Wikipedia article shows rhombuses as kites, but excludes darts. There are several related questions: Is a circle an ellipse?

I don't think we have to "decide" for all time, but I do think it is worth mentioning. My daughter would have had several of her geometry test questions marked wrong if she only consulted Wikipedia. Danieltrevi (talk) 14:15, 27 March 2019 (UTC)
 * I think the typical usage at the elementary and high school level is more or less as you describe (classifications are exclusive, so squares are not kites) and at any higher level of mathematics is usually inclusive (squares are kites). The reason for using inclusive rather than exclusive categorization is to avoid lots of silly special cases (e.g. with inclusive classifications we can state Varignon's theorem as: the midpoints of every quadrilateral form a parallelogram; with exclusive classifications we would instead have to say that sometimes it's a parallelogram, sometimes it's a rhombus, sometimes it's a rectangle, and sometimes it's a square, and readers would be left wondering why such a vague statement is even a theorem at all). So it bears mentioning that there are these two ways of doing things. But you have repeatedly added value judgements (it is usually one way but that some authors disagree) stated as fact with zero sources supporting those judgements. That is not how Wikipedia does things. Everything needs to be supported by references to reliable publications. So if you want to say that it is usually one way, you need a source that says roughly the same thing. Better would be to say what I have said above (lower level mathematics does it one way, higher the other way, and why) but again that needs a source. —David Eppstein (talk) 18:42, 27 March 2019 (UTC)


 * British schools usually teach the inclusive definitions. Is it only American schools that teach the exclusive ones?  ( Good teachers try to set unambiguous questions. )   Dbfirs  20:33, 27 March 2019 (UTC)

OK, I will try to find a source. Would a US high school geometry textbook be acceptable? (Pearson or McGraw-Hill). As I stated earlier, the article on the isosceles trapezoid has an almost identical statement, without a source. I don't recall ever even hearing about "kites" as a geometry term until this year. Danieltrevi (talk) 13:48, 28 March 2019 (UTC)
 * Would a US high school geometry textbook note the existence of both types of definitions and describe which usage is more common at which level of mathematics? That is the kind of source we need. I don't think finding a source that chooses and uses only one of the definitions is helpful for statements about which usage is more common. In particular I think that your addition of "Big Ideas Math" (Texas Ed., p. 401) as a source for this is so far off-topic as to be either incompetent or intellectually dishonest. That page gives a (pictorial) definition of kites but says nothing about the relation between kites and other kinds of quadraterals, let alone clarifying whether the definition should be inclusive or exclusive. —David Eppstein (talk) 18:57, 28 March 2019 (UTC)

I really think your "intellectually dishonest" comment was uncalled for. I think your comment was arrogant. I guess this is your pet page, and you don't tolerate disagreement. Danieltrevi (talk) 20:32, 28 March 2019 (UTC)
 * I am still waiting for proper sources to appear. —David Eppstein (talk) 20:55, 28 March 2019 (UTC)
 * This is your page, I guess, and "isosceles trapezoids" is someone else's page, so you have not undone my edits on that page. I think the discrepancies in how certain quadrilaterals are defined between US high schools and universities is worth mentioning. It is not worth abuse. I do not know if there is a source that says explicitly that there is a disagreement. Apparently, for you, a source that is in disagreement with the definition given in this page is not enough. Where is the source for the very first sentence of this article? -
 * In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
 * You could cite the reference "kite definition" in the "External Links" section, except that definition reads:
 * A quadrilateral with two distinct pairs of equal adjacent sides. A kite-shaped figure. (emphasis added by me.)


 * And why did you undo the citation to John Page in the link? That is the way he requested for his citations to appear.Danieltrevi (talk) 14:08, 29 March 2019 (UTC)Danieltrevi —(talk) 22:42, 28 March 2019 (UTC)
 * And as far as you waiting for "proper" sources to appear, I will not be providing them. I have pointed out what I think are several deficiencies on this page. If you, the self-appointed master of this page, do not think they are worth correcting, that is your call. Have a good day, and thank you for all you do for Wikipedia. -Danieltrevi (talk) 14:18, 29 March 2019 (UTC)


 * Just wanted to point out that the "kite definition" formerly in the external links section (I have removed it) was incorrect. The use of the word distinct is clearly in error. As software engineer John Page explicitly states, two pairs of adjacent sides are "distinct" if they have no side in common! This is confusing the concept of distinctness with a type of disjointedness. Two pairs can be distinct and yet share a common side, consider a triangle with one side designated as the base. The pairs of sides consisting of the base and one of the other sides, are two distinct pairs with a common side. If one views the pairs as sets consisting of two adjacent sides, then what he calls distinct is really the notion that the sets are disjoint (have no common element). Also, even if he used the adjective "disjoint", the case of the rhombus would not be ruled out. The only proper way to use the word distinct in this situation would be to rule out the possibility of considering the adjacent pair of sides A and B as different from the pair B and A. --Bill Cherowitzo (talk) 19:42, 29 March 2019 (UTC)
 * Thank you. You must remember, his website is aimed at high school math. This was confusing to me, and probably to many high school math teachers._23:25, 29 March 2019 (UTC)Danieltrevi (talk)
 * I suspect part of the confusion arises because some of the sources used the wrong word "distinct" rather than "disjoint", perhaps out of a feeling that "disjoint" was too technical. We want to say that a kite is a shape that has two disjoint pairs of equal adjacent sides. That is, the two pairs do not share any edges with each other. The sources that say that a kite has two distinct pairs of equal adjacent sides are wrong, because that definition would also apply to a 1-1-1-2 trapezoid (which I think we can all agree is not a kite). The trapezoid has two pairs of equal adjacent sides (the first 1-1 and the second 1-1), and these pairs are distinct (they are not the same pairs as each other) but they are not disjoint. Once we use the right word in the definition, we can then move on to finer distinctions, such as whether the decomposition into disjoint pairs must be unique or whether it is enough for at least one decomposition to exist. —David Eppstein (talk) 00:09, 30 March 2019 (UTC)
 * This misuse of the word distinct is very common among students in teacher preparation courses. We often have to start out emphasizing its use to increase the awareness of precision in mathematical language. The lesson is probably learned a bit too well and students begin to use the term indiscriminately because it seems to make their statements sound more precise. Overuse is not penalized as heavily as underuse, so the take-away seems to be "use it whenever in doubt". --Bill Cherowitzo (talk) 03:49, 30 March 2019 (UTC)

I added some material to the article (based on a source we were already using) distinguishing the two kinds of classification. It explains why one might prefer a hierarchical, inclusive classification (because that is what the source is about) but not what the advantages of a partitioning, exclusive classification might be. It also does not include the statements wanted to add, claiming that the hierarchical classification is more usual, because I still have yet to find any source that says so. So there's more that could be added here, although we should take care not to unbalance the article with material that is really about quadrilateral classification more generally and not about kites. —David Eppstein (talk) 17:29, 3 April 2019 (UTC)


 * During decades of teaching mathematics in high schools in the United Kingdom I never once knew of anyone teaching the "exclusive" definitions, but I knew thousands of pupils who believed that they had been taught those definitions. It is highly likely that in some cases they had been taught such definitions, because a large proportion of high school mathematics teaching is done by people who are not mathematicians, and who through ignorance teach stuff that is just plain wrong. (To give just one example, I came across some algebra revision sheets produced by a colleague who taught maths but whose initial training had been in another subject, and she included the identity (x + y)2 = (x2 + y2).) However, it is also certain that some of those who insisted that that Miss X or Mr Y had taught them the "exclusive" definitions were mistaken, because I knew that Miss X and Mr Y absolutely did not teach that. Is it really standard practice to teach the "exclusive" definitions in US high schools? As far as I know it is perfectly possible that it is, but it is equally possible that it isn't, and Daniel thinks it is because that is his personal experience, not typical.
 * My own view is that a mathematical technical term should be defined in the sense in which it is normally used and understood by mathematicians, which in this case is of course the "inclusive" case. If another meaning is standard in a particular area then it may be a good idea to mention it, but that other meaning should not take precedence.
 * It is, of course, not for us to decide what words "should" mean; rather we should follow accepted practice, whether we agree with it or not. However, for what it's worth there are excellent reasons why the "inclusive" definitions are preferable (which is why they are the ones accepted by mathematicians). A square is a type of rectangle, and a rectangle is a type of parallelogram, and to define them otherwise would be unhelpful, for numerous reasons, including the one which David Eppstein has described above. The editor who uses the pseudonym "JamesBWatson" (talk) 20:50, 3 April 2019 (UTC)


 * I was very surprised to find that yes, it is indeed the case, that in US high schools the exclusive definition is the one that is commonly taught. It started with a worksheet she had listing the properties of various quadrilaterals, and you had to choose "always", "sometimes", or "never." For kites, the correct answer to the question "all four sides are congruent" was "never". I asked, "well, what if the kite is a rhombus?" "A kite is never a rhombus," according to her notes, and US high school texts. "A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent." (I am sorry, the links I placed don't seem to be working. Google "US high school geometry textbook" and you can find some free online textbooks. https://bim.easyaccessmaterials.com/index.php?location_user=cchs might work. I chose "Texas" and then the kite definition is page 405.
 * I thought many other homework help sites also used the exclusive definition, but upon review, I see I was confused because of the uses of the words "disjoint" and "distinct". Apparently, US textbook authors made that same mistake. If you Google "quadrilateral family tree" you will see the exclusive definition predominating.Danieltrevi (talk) 22:41, 4 April 2019 (UTC)

tangency

 * The kites are exactly the quadrilaterals that are both orthodiagonal and tangential. In a tangential quadrilateral, the two line segments connecting opposite points of tangency have equal length if and only if the quadrilateral is a kite.

If this is about tangency to an inscribed circle, that ought to be specified. —Tamfang (talk) 05:26, 12 January 2011 (UTC)
 * You did read the paragraph immediately above this one, no? —David Eppstein (talk) 05:38, 12 January 2011 (UTC)


 * Yeah, belatedly (d'oh!). It would be more obvious if the paragraph break were removed. —Tamfang (talk) 05:39, 12 January 2011 (UTC)
 * My idea of the structure here is that the first paragraph of the section describes properties related to the diagonals, the second paragraph describes paragraphs related to the inscribed circle, and the third synthesizes both of the previous paragraphs by combining the diagonals and the circle into a characterization of kites. But I don't mind if you want to restructure it. —David Eppstein (talk) 17:35, 13 January 2011 (UTC)

A Commons file used on this page has been nominated for deletion
The following Wikimedia Commons file used on this page has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 17:53, 18 May 2019 (UTC)
 * Rhombicdodecahedron.jpg

Degrees or radians
> One of them is a tiling by a right kite, with 60°, 90°, and 120° angles.

> kite with angles π/3, 5π/12, 5π/6, 5π/12.

Some angles are quoted in degrees; some in radians. I prefer degrees. JDAWiseman (talk) 16:08, 9 September 2020 (UTC)

Aren't squares kites too?
A square can be split into two adjacent sides of equal length too, I want to know why it wouldn't be considered as a kite. - S L A Y T H E - (talk) 16:27, 27 January 2023 (UTC)


 * Why do you think they wouldn't? Our article says, explicitly, "They include as special cases ... the squares, which are also special cases of both right kites and rhombi." —David Eppstein (talk) 18:16, 27 January 2023 (UTC)
 * It doesn't seem to be included at the "special cases" section though. Thanks anyways :) - S L A Y T H E - (talk) 18:30, 27 January 2023 (UTC)

"Diameter" meaning what?
The word "diameter" appears three times in the article, in the context of "Among all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter is an equidiagonal kite with angles 60°, 75°, 150°, 75°."

Diameter of what? The inscribed circle? If so, then this statement is false, because I can construct a kite with an unlimited ratio of perimeter to diameter (a really long pointy kite with a small circle inscribed).

Or is this restrocted to only equidiagonal kites? If so, then that isn't what the sentence says.

The article should clarify what "diameter" means here. Or clarify that sentence, both in the lead and in the body text. ~Anachronist (talk) 22:21, 11 August 2023 (UTC)


 * Diameter here obviously means the largest distance between points (diameter = literally "measure across"). Your very pointy kite has ratio of perimeter to diameter of about 2, which is much smaller than the one described for which the corresponding ratio is >3 (for a square the ratio is $$2\sqrt{2} \approx 2.83$$). The article gives sources in the relevant section later on. –jacobolus (t) 23:10, 11 August 2023 (UTC)
 * If you click through the wiki-link to diameter you will find: For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the is often defined to be the smallest such distance. Both quantities can be calculated efficiently using rotating calipers. –jacobolus (t) 23:19, 11 August 2023 (UTC)
 * That second definition is correct but more technical than necessary. The definition you quoted earlier, the largest distance between any two points, is simpler. —David Eppstein (talk) 02:00, 12 August 2023 (UTC)
 * Thumbs up. –jacobolus (t) 02:14, 12 August 2023 (UTC)

Tetrahedron has kite-shaped faces?
@David Eppstein. The article says trapezohedron has kite-shaped faces. But what about the digonal trapezohedron (known as the regular tetrahedron)? It has triangular faces instead of kites. Dedhert.Jr (talk) 13:14, 15 July 2024 (UTC)


 * @Dedhert.Jr when you call
 * it a digonal trapezohedron you are really thinking of it's faces as being degenerate kites with 180 degree angles at the two poles of the trapezohedron, at the midpoints of two opposite edges of the tetrahedron. —David Eppstein (talk) 00:09, 16 July 2024 (UTC)
 * =@David Eppstein Thanks. But what if this is happen to non-mathematical readers after they realized it is not kite-shaped face? What I am pointing here is many people do not understand how does regular tetrahedron being digonal trapezohedron, a degenerate case for trapezohedron? What is degenerate kite means according to them? To put it in plain, writing about the degeneracy of a geometric figure would help readers to understand even more. Dedhert.Jr (talk) 00:42, 16 July 2024 (UTC)
 * Degeneracy (mathematics) could definitely be improved, with more concrete examples including pictures etc. Anyone who is interested should definitely feel free to work on that. –jacobolus (t) 02:14, 16 July 2024 (UTC)
 * The only way a reader could see this degenerate example without seeing the discussion in trapezohedron explaining how it is degenerate would be to see the huge multi-screen-wide table of irrelevant data about trapezohedron somehow copied from but not quite the same as in the Trapezohedra template, which I have just removed as irrelevant. We already have a picture of some trapezohedra (the dice); why do we need so many more? —David Eppstein (talk) 09:37, 16 July 2024 (UTC)
 * That's another good option. However, when you are saying huge multi-screen-wide table, and the discussion about excessive tables in WT:WPM, it reminds me of how I was trying to restructure and expand the article Bipyramid in which tables were converted into multiple images. I don't think these could be applied in this article in the same way because of GA criteria: images are relevant to the topic and provided with suitable captions. Dedhert.Jr (talk) 14:40, 17 July 2024 (UTC)