Talk:Rhombus/Archive 1

Confusing, bad english...

Things I don't like: the 'Two Definitions' heading and the bad English in the Properties section (a few stray "the"s for one). Intro could also use another wikilink or two. Shouldn't be hard to fix - I'm just too tired at the moment to do so. Tmandry 04:05, 19 December 2006 (UTC)

I removed the "two definitions" statement. A square is certainly a rhombus mathematically (just as it is also a rectangle and a parallelogram). I realize that a square is not a "typical" rhombus and that we generally distinguish between a "square" and a "diamond" colloquially (although a baseball "diamond" is, for all intents and purposes, a square). However, a statement that a rhombus is NOT a square should be backed up by a citation. Paul D. Anderson 20:30, 21 December 2006 (UTC)

"the different symmetry as the rhombus" ?

"The rhombus has the different symmetry as the rectangle..." It may be something mathy that I don't understand, but this seems really odd to me. Peter Delmonte 17:51, 23 November 2006 (UTC)

Fixed. No mystery here — it was just someone being obtuse. That can't be right? 16:42, 13 February 2007 (UTC)

The perfect picture

Your website gives me lots of ideas for my homework when I struggle. 67.83.26.245 22:38, 29 May 2007 (UTC)

Poorly written

This entry is poorly written, confusing and contains grammatical errors. 207.172.214.192 13:18, 28 October 2007 (UTC)

You're too hard on yourself. 81.157.44.112 (talk) 15:43, 25 July 2008 (UTC)

LOL! -70.251.131.28 (talk) 20:02, 29 January 2009 (UTC)

We're forgetting something

Um, I noticed that this page has a proof for the fact that the diagonals of a rhombus are perpendicualr to each other, but what about the fact that the diagonals of a rhombus also bisect the angles of the rhombus as well? —Preceding unsigned comment added by King Bong (talk • contribs) 11:51, 15 February 2009 (UTC)

== Pointercan be found too. I do not know how to do this. :) --andy 80.129.124.140 17:17, 12 November 2005 (UTC)

Posted proofs are inaccurate...

The first couple proofs posted (AC = AB + BC followed by BD = BC + CD = BC - AB), when based on the illustrated rhombus are clearly false. I'll summarize the inaccuracy of the first one (as the second's faults become readily apparent thereafter).

The rhombus pictured in the article is essentially made up of four right triangles. The right angles of these 4 triangles share the same vertex (in the middle of our rhombus, we'll call it X). AB and BC are both hypotenuses of X. AX and XC (our bisecting line) are both Catheti of Right Triangles. Based on the most fundamental Right Triangle Theorem (Pythagoras), the sum of two catheti, each from seperate Right Triangles, could never be equal to or greater than the sum of those two Right Triangles' hypotenuses.

No doubt, there's not a more efficient way of demonstrating this, but it's been 14 years since I've even thought about a geometry proof, so it's a little clunky. —The preceding unsigned comment was added by K10wnsta (talk • contribs) 05:52, 9 March 2007 (UTC).

Using the inner product as part of the proof seems like cheating. I'd prefer to have seen an ancient greek proof based on pure geometry, not vector mathematics. —Preceding unsigned comment added by 195.137.115.172 (talk) 01:41, 5 February 2009 (UTC)

Can I just say that you are wrong when saying that the proofs are incorrect, because there is nothing, as far as I can see, that isn't right in certainly the first proof; when they are talking about AB, BC or AC they are not talking about lengths but rather vectors, hence the arrows over the top signifying direction. I'm afraid that K10wnsta has got completely the wrong end of the stick! 80.4.6.189 (talk) 20:37, 5 March 2009 (UTC)

Squares?

The article states that squares are also rhombi, which was always my belief. However, the rhomboid article contains the following:

"Euclid introduces the term in his Elements in Book I, Definition 22,

Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia."

This appears to contradict the information contained in the rhombus article. Is there a geometry teacher out there who might verify which account contains the correct information? -70.251.131.28 (talk) 20:08, 29 January 2009 (UTC)

You are quite correct, this is exactly how Euclid defined the terms, and there are probably a few teachers of geometry, especially those who read the original Greek, who would wish to retain Euclid's usage. However, Euclid didn't actually use the word rhomboid - he preferred parallelogram, and, unfortunately, the words have changed their meaning over the last 2000 years, and most teachers now teach inclusive definitions, so the term rhombus usually includes squares. You will be pleased to know that the word oblong has not changed its meaning (but is seldom used by mathematicians). Fortunately, we all agree over the meaning of square (though squares in Reimann space often don't look square), but the word rhomboid means different things to different people, so should not be used without explaining the sense intended. The situation over the confusing transposition of meaning for trapezium and trapezoid (by Charles Hutton) really needs sorting out, but everyone insists on sticking to the definition they were taught in school, so it will be many years before everyone can agree. Sorry to confuse you further! Dbfirs 21:29, 29 January 2009 (UTC)

LOL..thanks for the info. So, would you (personally) refer to an object that qualifies as a 'rhombus' (such as a square) as being 'rhomboidal'? Or would the correct term be 'rhombal', perhaps? -70.251.131.28 (talk) 16:00, 30 January 2009 (UTC)

Personally, I wouldn't use either adjective (without first explaining the meaning) because the few who might understand the words would probably also know that they are ambiguous. Why would I need the adjectives when I have nouns? A square is always a rhombus by modern definition. It is not a rhomboid by Euclid's definition and might or might not be by modern usage (depending on whom you ask). And just to confuse the situation further, some people believe that Euclid never existed as a man! Dbfirs 08:58, 5 February 2009 (UTC)

In any case, it says if a rhombus has right angles it's a square but that actually just makes it a rectangle... —Preceding unsigned comment added by TMP1080 (talk • contribs) 00:30, 12 February 2010 (UTC)

Please think again about that. A rhombus has four equal sides. Can it be an oblong (non-square rectangle)? Dbfirs 08:48, 12 February 2010 (UTC)

Kites and perpendicular diagonals

The article states that "In general, any quadrilateral with perpendicular diagonals is a kite". However, this is not the definition given in the Kite article, and in fact, it is easy to imagine a quadrilateral with perpendicular diagonals that is not a kite (that is, a quadrilateral with two pairs of adjacent, same-length sides) : simply take a kite and stretch it by moving one of its vertices in a given direction, keeping the diagonals perpendicular and the other three vertices fixed. So, is the article in error or am I interpreting it incorrectly ? 87.88.56.250 (talk) 01:24, 23 August 2010 (UTC)

The statement is correct incomplete, and could be an alternative definition for a kite, though it is not the usual definition. The definition given at the kite article and this definition (as amended) are equivalent. In your thought experiment of stretching a kite, you will always obtain another kite. Dbfirs 07:42, 23 August 2010 (UTC)

I remain unconvinced. A stretched kite no longer has two pairs of equal-length adjacent sides, which directly contradicts the definition in the kite article : in fact, you can stretch a kite so that no two sides have the same length, while keeping the diagonals perpendicular. I agree, however, that a kite always has two perpendicular diagonals. Furthermore, the Quadrilateral article mentions "orthodiagonal quadrilaterals" at one point, to refer to quadrilaterals with perpendicular diagonals, suggesting that these quadrilaterals are not always kites. 87.88.56.250 (talk) 02:04, 24 August 2010 (UTC)

Please accept my apologies. I must have been suffering from tunnel vision because I imagined stretching only along the axis of symmetry. I've amended the statement in the article, and also my reply above (retaining the original so that other readers can see my error and the reason for your response). Are you happy with the amendment? Dbfirs 06:29, 24 August 2010 (UTC)

The articles no longer conflict with each other, and I have retained faith in my own sanity :) Thank you for the quick replies and the edit. 87.88.56.250 (talk) 06:43, 24 August 2010 (UTC)

I'm horrified to see that the error has been there for seventeen months and I must have read it several times without noticing the mistake. Have you spotted any other errors in basic articles? Dbfirs 06:54, 24 August 2010 (UTC)

To be honest, I just stumbled upon this one and managed to convince myself that it was really erroneous, though this usually doesn't happen much - I'll be sure to tell you if I see any other issues. Don't be too hard on yourself though, tunnel vision is something that is unavoidable, especially with such things as editing encyclopedias. 87.88.56.250 (talk) 07:09, 24 August 2010 (UTC)

"In mathematics" is a bad section title

"In mathematics" is a bad section title for a section of an article that's entirely about mathematics. Anyone have an idea for a replacement title? Maybe "Other properties"? Duoduoduo (talk) 21:39, 22 May 2012 (UTC)

Convexity

A recent edit removed the stipulation that an equilateral quadrilateral must be convex to be a rhombus, with the edit summary A quadrilateral with four equal sides is necessarily convex, so including that in the definition is redundant, and misleading. I'm reverting this because (1) it's unsourced, and (2) there exists a class of counterexamples--nonconvex equilateral quadrilaterals. Let side 1 meet side 2 at a non-180° angle; let side 3 coincide with side 2 but in reverse direction; and let side 4 coincide with side 1 but in reverse direction. This is a legitimate counterexample despite being degenerate in the sense of having zero area. It's not convex since a segment connecting a point on side 1 with a point on side 2 (other than their shared vertex) goes outside the polygon. Duoduoduo (talk) 16:32, 6 June 2012 (UTC)

I'm an old school mathematician so I didn't even realize that self-intersecting polygons would be considered, until I finished the edit and then happened to check the "quadrilateral" page and saw the references to "simple" and "complex" polygons. So I made a second revision in which I added "simple" (which would be a weaker requirement if we were discussing polygons in general, but is equivalent in this case). But then I thought about it and realized that the only self-intersecting equilateral quadrilateral would be the type of degenerate case you mentioned (although the angle between the first two sides could be 180 degrees (allowed under some definitions of polygon), or 0, in which case it's even more degenerate, and all four sides are coincident), and thought that that couldn't possibly be considered a polygon, so I undid that revision.

The addition of "convex" in the definition on this page was an unsourced edit on Sept 11 2011, two days after the same user made analogous edits for the "parallelogram" page. I think "simple" is a better criterion, because 1) it's (generally) a weaker requirement, and 2) the whole concept of "complex" or self-intersecting polygons seems to be a recent development (the "complex polygons" page only refers to its use in computer graphics). It's unsettling to have to start making changes in basic definitions in a 2000 year old subject just to fit the conveniences of a single specialized modern application, so let's mark the distinction where it truly lies. Jmmahony (talk) 09:15, 13 June 2012 (UTC)

Looks good! Duoduoduo (talk) 14:32, 13 June 2012 (UTC)

Is the rhombic icosahedron not one type of rhombus?

Check out this video of a rhombic triacontahedron being created to see what I mean: http://vimeo.com/7786185 — Preceding unsigned comment added by 137.205.113.132 (talk) 22:52, 11 February 2014 (UTC)

I've moved your question to the end, where new questions are normally placed to preserve the time sequence. A rhombic icosahedron is a 3-D solid, but each of its 20 faces is a rhombus. Each of the 30 faces of a rhombic triacontahedron is a rhombus, too. Dbfirs 00:40, 12 February 2014 (UTC)

p's and q's.

although used throughout the article (describing the parallelogram law, and in calculating its area), i can't find a labelled diagram explicitly showing what is p and what is q. like this diagram from wolfram.

when diagonal in the common usage seems to mean "any line that doesn't go straight up and down, or flat left to right like the horizon", i can see extra confusion for the less spatially inclined seeing as in the most common presentation of rhombuses has p and q in the somewhat less intuitive orientation*.

• w.r.t. general definition of diagonal.

∋sensorsweep 01:16, 17 November 2014 (UTC)

I suppose that there might be the odd reader who doesn't understand the meaning of the word diagonal, and fails to click on the repeated link or to understand the definition, but I wouldn't think there are many. I agree, though, that a little diagram would help those few. Any volunteers? Dbfirs 07:40, 17 November 2014 (UTC)

Etymology

Isn't it from the rhombos, a musical instrument similar to the bull-roarer?[1]Kortoso (talk) 20:15, 4 January 2017 (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:

• Rhombicdodecahedron.jpg

Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 17:54, 18 May 2019 (UTC)