• OwOarchist@pawb.socialEnglish
      76·
      10 days ago

      I went up to Calculus I in college (along with some physics and engineering), and I’ve done a bit of amateur math outside of school … but the concept of a rhombus was still used exactly zero times.

      The engineers prefer triangles, the physicists prefer circles, and the pure mathematicians are usually dealing with weird shapes that don’t even have names. Who uses the rhombus?

      • disorderly@lemmy.world
        32·
        10 days ago

        Right there with you, I didn’t use it in analytical geometry, calcs 1-3, diff eqs, or numerical methods. I don’t think it would have shown up in my other math classes either. I’m pretty sure the rhombus is nothing more than a happy shape.

        • HeHoXa@lemmy.zip
          3·
          10 days ago

          What’s numerical methods all about?

          I mean I think I can intuit a little and could Google a lot, but hearing from someone who seemingly somewhat recently studied is a unique chance.

          • disorderly@lemmy.world
            15·
            10 days ago

            As the other poster succinctly said, it’s about iterative solving problems. What might not be obvious is where you want to use this.

            Let’s say you are holding onto a continuous, all-metal cooking pan’s handle and you turn on the burner; at what second will it be too hot to hold? If we assume the pan is starting at 20 C and it’ll be too hot for your leathery, lemmy-browsing hand at 100 C, then we at least have some basic bounds on the problem, but how do we think about the middle parts?

            We could say that the burner is putting out about 5 kW of energy (or more simply, that the pan’s bottom has a fixed input of 5 kW (a so-called boundary condition). With a basic equation translating energy input into temperature (factoring in specific heat), we at least know the temperature of the bottom of the pan at a given moment, but what about the top of the pan and, most importantly, the handle? The temperature in these places isn’t climbing because they’re getting licked by flames, but due to thermal conductivity away from the bottom.

            Thermal conductivity is actually one of the simplest questions in partial differential equations (PDEs), and is addressed with the aptly named heat equation. In extremely casual terms, the heat equation (du/dt = L u) is saying that the heat at a given position is determined by its past heat plus the past heats of positions around it. Our job as mathematicians is to express our problem using a so-called weak form of the heat equation that makes it possible for an iterative solution.

            We can solve weak form equations with a framework like the Finite Differences method (which is a little dated but easier to understand than other methods, and also still quite effective). This very basically means we’ll create a fixed grid of points, then express the relationships between them with algebra.

            Once we have our algebraic mesh and we are happy with all of our boundary conditions, we can start the simulation. We watch as the temperature immediately shoots up on the bottom of the pan (followed soon after by the top and edges), then as heat slowly transfers up the handle until it reaches 100 C at the end.

            In doing these problems, we make as many simplifications as possible in the boundary conditions, because the equation’s solution space is unfathomably large. Everything we can do to constrain it (easy heat source, exact physical parameters of our materials, etc) shrink the solution space closer to one that matches our actual problem.

            As a final thought, lots of very bright people have spent entire careers designing heatsinks using numerical methods, so don’t take my description of the heat equation as an easy problem to mean it’s not a great line of inquiry, but rather that the field is really fucking hard. Anyone who does this stuff can, in fact, hold a 90 C pan handle because their tolerance for pain is astronomical.

          • Gork@sopuli.xyz
            11·
            10 days ago

            It’s all about solving things iteratively. Usually applied to how computers solve for things.

      • agamemnonymous@sh.itjust.works
        8·
        10 days ago

        A rhombus is just an equilateral parallelogram, and parallelograms are the easiest way to approach vector cross products. And you’re 3/4 of the way there when you do tip-to-tail vector addition. They should have come up at least a couple times in geometry. Rhombi pop up as faces in lots of polyhedra, and tiles in lattices. I don’t know much about crystallography, but I’m sure they make an appearance.

        • ulterno@programming.devEnglish
          2·
          10 days ago

          Now that I think of it, when doing lattice structures in Chemistry, many sections would have given rhombuses.
          But still, never used the name even over there.

    • flamingo_pinyata@sopuli.xyz
      18·
      10 days ago

      They’re not really mentioned in more advanced math. It’s all polygons.

      Ok, triangles are often treated as a special case. But for anything else it’s a n-sided polygon.

      • Anna@lemmy.ml
        2·
        10 days ago

        Nah in my experience everything is a circle. You see π even in places you don’t expect

      • Grail@multiverse.soulism.netEnglish
        2·
        10 days ago

        You mean regular polygons. A rhombus is an irregular polygon. Triangles are also all polygons. An equilateral triangle is a regular one.

    • M137@lemmy.today
      2·
      9 days ago

      It’s not even doing math, just watching science videos etc. is enough to hear the word every now and then. This is surely a person who has no interest in learning overall.

  • Mycatiskai@lemmy.ca
    10·
    10 days ago

    Every 3 ft square box that you shoved a bunch of 3.25 ft long irregularly shaped items into then closed the flaps on is a rhombus.

  • Funkt4st1c@lemmy.worldEnglish
    9·
    10 days ago

    A rhombus, otherwise known as a diamond. Its one of the more popular shapes past star, triangle, circle, and square.

  • treesquid@lemmy.world
    9·
    9 days ago

    Take a square. Lean it to the side. Rhombus. Take a diamond, let it fall on one of its sides. Rhombus. The world just keeps a-rhombusin, you just stopped a-noticin’