• treesquid@lemmy.world
    9·
    6 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·
    6 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:

    • Batman@lemmy.world
      3·
      6 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”

    • Noxy@pawb.socialEnglish
      2·
      6 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

    • tetris11@feddit.ukEnglish
      1·
      6 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·
        6 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.

  • AlteredEgo@lemmy.ml
    6·
    6 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·
      6 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·
      6 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.

  • Nautalax@lemmy.world
    3·
    7 days ago

    There is an evil invasive plant called Sida rhombifolia that invades local habitats and is obnoxious to pull over here. Guess what shape the leaves are

    edit: Acalypha rhomboidea is on the side of justice here though