25 thoughts on “Rhombus

  1. I can’t prevent my earworm generator from trying to sing “The wheels on the rhom-bus go round and round”. But that is so completely wrong! If there’s something a rhombus is not, it’s “round”.

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  2. Wait, is it normal not to think about rhombi? Like when you see a rhombus, you don’t acknowledge it being a rhombus like you would a square or a circle?

    In other words, there is absolutely nothing relatable in this comic for me.

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  3. There was a B.C. strip in which Thor had invented the triangular wheel (as an improvement over his previous square wheel). When asked why it was better, he replied “One less bump.”
    P.S. unfortunately the GoComics B.C. archive is incomplete, so I can’t provide a link to the image.

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  4. @Powers,
    I suspect that most people don’t think of the word ”rhombus” when they see that type of quadrilateral shape.
    They more likely think “diamond”, as in “hearts, diamonds, spades, and clubs”.

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  5. So to Kilby’s comment (which I read before I read the comic in question): this sort of highlights the whole @%#$ing problem with education and our resignation to it rather than feeling outrage! The BC comic he quotes shows exactly backwards understanding — the more bumps the better if you are trying to gradually approach the functionality of a wheel. This seems counter-intuitive at first, until you more deeply understand that it is not just number, but number coupled with intensity of the bump that matters in achieving wheel-like functionality — better to have many, many little bumps, none of which can totally stop the rotary action, than to have few bumps that are of such magnitude that they completely disable the circulatory action. An eight-sided “wheel” could be made to roll, a sixteen sided one even moreso, whereas a four-sided one can’t, and even less so a three-sided one.
    Why the @!#$$% aren’t we teaching thinking ability? And why are we content to laugh ha ha at the fact that I can’t remember what a rhombus is even though I knew it once, but it turned out to never be useful, instead of raging that they are wasting our children’s time and brain capacity teaching this kind of tripe?!

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  6. TedD, the diagram has some weirdness, such as the directed edges; and does not indicate the edges have equal lengths. So you are correct, up to a point: the diagram does not show us that the figure must be a rhombus. But if we are asking about the figure as concretely drawn, it certainly looks to be equilateral, and hence a rhombus. (And that’s all that would be required — though often shown oriented in a tall narrow diamond or lozenge shape, that is not required to count as a rhombus.)

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  7. That figure in panel 1 looks like a rhombus to me. The sides appear equal length; the diagonals appear to meet at their own midpoints; and the diagonals are explicitly shown to be perpendicular.

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  8. My bad. I neglected the perpendicular diagonals.

    I’m assuming the arrows on the edges of the rhombus indicate which ones are of the same length. It is a very common notation on diagrams of shapes to use marks of one sort or another to indicate this. The arrows indicate opposite sides are of the same length, but not necessarily adjacent sides. However, there is a theorem that if the diagonals of a parallelogram are perpendicular, it is a rhombus. I’m assuming there is also a theorem that indicates if the opposite side of a quadrilateral are equal it is a parallelogram, but I don’t recall that one off the top of my head. But I’ll assume that is true, but this figure is a parallelogram with diagonals perpendicular to each other, thus a rhombus.

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  9. The bigger problem is with trapezoids. In the U.S. a trapezoid is a “quadrilateral with two parallel sides”, but in Britain, it’s a “quadrilateral with no parallel sides”.

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  10. Maybe what I was taking to be arrowheads, showing the sides as directed edges for some reason, are really just similarity markers. So BA is the same length as CD, and BC is the same length as AD. With that, and Powers’s observation that the diagonals are marked perpendicular, is that enough for us to prove all four sides are equal? Or that each pair of opposite sides are parallel? Either would make this a rhombus conclusively.

    (Yes, the sides appear equal length; and the crossing diagonals appear to meet at their midpoints. But that just means this concrete realization is a rhombus, not necessarily the general figure given.)

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  11. I think my follow up post was eaten.

    It is a rhombus. I missed the perpendicular diagonals.

    The arrows indicate which sides are of the same length. In this case, opposite sides are the same length, adjacent sides not necessarily. However, a quadrilateral with equal opposite length sides is a parallelogram, I believe. I’m not certain of that theorem, but I seem to recall that is true. I am certain that a parallelogram with perpendicular diagonals is a rhombus. So, assuming a quadrilateral with equal opposite sides is a parallelogram, this is a rhombus.

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  12. Ah, good point! I’m guessing the arrowheads are markers of parallelism rather than congruence. So the arrows would show that this is a parallelogram, and the right-angle at which the diagonals meet can then prove it’s a rhombus.

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  13. In high school, we had a quiz thing. One question was something like, “another name for a rectangular rhombus”. I was first to the answer of “a square”.

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  14. Something is happening to my posts… weird.

    I’ve tried to rescind my statement twice it isn’t a rhombus. I saw the statements after hitting “Post Comment”, but now that I’ve come back, they are gone.

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  15. Heraldry? I associate them with cough medicine, perhaps from the William books (Richmal Crompton). But rhombus, diamond or lozenge, it’s all the same.

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  16. Okay, I checked for myself, at https://www.heraldsnet.org/saitou/parker/Jpglossl.htm . Hard to read with the insistent background image, but legible in the end. Below several screens for the “Lions” entry we do get this entry:


    Lozenge, (fr. losange): this charge is of a diamond shape, the diameter being about equal to each of the sides; in the fusil, which is similar in shape, the diameter is less than each of the four sides, thus giving it a narrower appearance. When a lozenge is voided, or percée, it is always in modern heraldry blazoned as a mascle, q.v.

    followed by groups of about a dozen examples, like “Gules, seven lozenges conjoined vaire, three, three, and one–DE BURGO, Bp. of Llandaff, 1244-53”.

    The note giving the French as “losange” reminded me of Films du Losange, which was the company behind Eric Rohmer, and whose logo was indeed a rhombus in diamond orientation. (Eric Rohmer, now that’s a name for the “Do we think he’s still alive?” inquiry.)

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  17. Fun. And the Losange Firm (“la firme au losange”) is the Renault car manufacturer.
    Rhomer is dead but my mother is a fan, so easy.

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  18. TedD, we hear you. It can be frustrating when something like a correction gets delayed in moderation.

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