• treesquid@lemmy.world
    9·
    3 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’

  • gandalf_der_13te@feddit.org
    81·
    3 days ago

    oh they don’t appear again, but its generalization, the parallelepiped, does:

    it’s used to calculate volumes of curved objects. basically you chop down the object into a lot of small parallelepipeds (mentally), and then calculate the volume of each of them small things and sum over them. Done.

    to calculate the volume of a parallelepipede, there’s a surprisingly simple mathematical formula. If you have the vectors for the three sides a, b, c, then the volume V = (a × b) · c, where × is the cross product and · is the dot product. it’s very simple and an effective way to calculate volumes of curved / deformed objects.

    Links:

    • Noxy@pawb.socialEnglish
      2·
      3 days ago

      where × is the cross product and · is the dot product

      pardon my ignorance but what the fuck is a “cross product” or a “dot product”? I assumed at first this was multiplication, but then I saw the dot and realized this isn’t anything I’ve ever been taught

    • Batman@lemmy.world
      3·
      3 days ago

      Sometimes I think about parallelepipeds then when I reassociate I’m smiling and my fiance is visibly wondering what I’m thinking about. “Don’t worry hun, parallelepipeds again”

    • tetris11@feddit.ukEnglish
      1·
      3 days ago

      it’s used to calculate volumes of curved objects. basically you chop down the object into a lot of small parallelepipeds (mentally), and then calculate the volume of each of them small things and sum over them. Done.

      For anyone not quite getting this (like me), to calculate the area under a curve in 2D we were taught to cut it into tiny thin rectangles and sum those up; intergration when those rectangles have a width tending to 0.

      For 3D (e.g. a pond ripple) or higher curves, a simple rectangle wont cut it as the length of the rectangle might only get the top of a wave, but not capture the crest of it tangential to it. So you create slopey rectangles to approximate that space, and bring the limit to zero to get the area (I think).

      My only confusion now is, if I’m deforming a rectangle from one side to approximate the curve just above it, am I not also deforming the bottom of that rectangle in the same way (for the parralel strcture to hold true), and creating a forgotten space just above the axis plane?

      • gandalf_der_13te@feddit.org
        2·
        2 days ago

        well, almost. it’s a bit different than that.

        what you mean is this:

        you approximate an integral with a lot of small thin rectangles, but if the curve’s not entirely rectangular, there’s gonna be some error, which becomes smaller as the rectangles become smaller. this can be ignored if the rectangles are thin enough. and it’s not what i meant.

        what i meant is something like this:

        you take a piece of elastic fabric, and paint some squares on it. now, if you stretch the fabric, the squares change shape, they become approximately parallelepipeds. this is a good approximation. now, if we want to calculate the total area of that fabric (after stretching), we can calculate the area of each of the small parallelepipeds (which is easy to do with the formula in above comment) and then sum them.

    • OwOarchist@pawb.socialEnglish
      94·
      5 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
        37·
        5 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·
          5 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·
            5 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
            12·
            5 days ago

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

      • agamemnonymous@sh.itjust.works
        10·
        4 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·
          4 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.

      • SailorFuzz@lemmy.worldEnglish
        131·
        5 days ago

        This is true for most parallelograms and later polygons.

        Daughter just went through parts of middle school that seemed to focus on things like rhombuses and trapezoids. The only thing I"m thinking, as an engineer, is when was the last time I gave af about any of those shapes? I would just reduce them to triangles and rectangles.

        Trig skills are WAY more useful than knowing how to calculate specific polygon shapes… I don’t mean to say that middle schoolers should be learning trig… just that the time spent learning how to do specific shapes is a literal waste of time that they could be using to prepare for later things (like trig).

        • gibmiser@lemmy.world
          8·
          5 days ago

          As someone in education i would bet money that since it is a vocabulary word with a simple definition in a subject that is hard to teach, it is included to make things easier on the teachers and students. Mind you easier isnt often a good thing, and in this case I’d say its lazy and irresponsible to focus on things that don’t scaffold well or have much practical use

          • OwOarchist@pawb.socialEnglish
            4·
            4 days ago

            Maybe it shows up in some of the dreaded standardized tests, and that’s why they’re sure to teach it?

    • flamingo_pinyata@sopuli.xyz
      20·
      5 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.

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

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

      • Anna@lemmy.ml
        2·
        4 days ago

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

    • M137@lemmy.today
      2·
      4 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.

  • AlteredEgo@lemmy.ml
    6·
    3 days ago

    Imagine living as a farmer in medieval Europe near a small village and you make MOST of your shit yourself or with help from the local blacksmith. You’d use all kinds of things and ideas that we don’t use any more. You need to be creative to solve your daily problems and find ways to do stuff efficiently. Like imagine you’d need to dig out a bit of earth for an “almost square” and need to calculate the area and volume of earth you’ll have to move.

    I’m not sure what I’m trying to say, but I think modern education is wasted on the modern human.

    • Jankatarch@lemmy.world
      6·
      3 days ago

      We are not curious enough. Dopamine hit of figuring out a cool thing requires lots of time, meanwhle videogames and movies are guaranteed in short term.

      We are not to blame tho, time to spend bored is simply not something we have; every other moment of our life will be either at work, preparing to go work, or driving to work, afterall.

      I predict the farmer dug that square on snow instead of dirt. They certainly weren’t farming during mid-winter. Must be boring. I will still be labeling amazon boxes this december.

    • CrimeIsLegalNow@ani.social
      4·
      3 days ago

      The point of the modern grade school education is to give any and every student enough of a education in any given topic to specialize in any field afterwards, depending on interest and opportunities, as well as create voting citizens that can understand at least the basics of any given social debate.

      Modern education isn’t wasted. Some people just waste it afterwards.

      And some people who want to destroy it to keep everyone as ignorant as your medieval peasants pretend that they don’t understand any of that.

      Also smiths would literally just do that on vibes lmao.