this post was submitted on 08 Sep 2026
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A meme is an idea, behavior, or style that spreads by means of imitation from person to person within a culture and often carries symbolic meaning representing a particular phenomenon or theme.
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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?
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.
Ohh! Calculating area, not volume under the curve -- I see, thank you