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unconed / MathBox.js

MathBox is a (work in progress) library for making presentation-quality math diagrams in WebGL.
MIT License
1.94k stars 126 forks source link

Example request: Plotting an integral #23

Closed ajvincent closed 10 years ago

ajvincent commented 10 years ago

Hi, guys. This project is one I'm going to get very excited about; though I'm not ready to use it (and won't be for quite a while), I can see it lays the foundations for something I want very badly.

My request: can someone put together an example of a function plot, along with the plot of its integral? Specifically, filling in the area between the plotted curve and the x-axis with the same color as the curve, with maybe 10-30% opacity. Bonus points for drawing it as a Riemann sum of rectangles first, and narrowing the rectangles as the partition limit approaches zero. Major kudos if this example can be part of a proof of the Fundamental Theorem of Calculus.

I'd do it myself, except I'm hip-deep in my own projects.

unconed commented 10 years ago

There is a much better visualization of this in my calculus article on acko.net. Don't narrow the rectangles until they vanish, normalize them so they don't.

waldyrious commented 10 years ago

btw, a few days ago I came across a simple but very effective illustration of integration, here: http://worrydream.com/KillMath/#anecdote

Also, the visualization @unconed is talking about is here (pointing it out since the title doesn't mention "calculus"): http://acko.net/blog/to-infinity-and-beyond/ - specifically, the animated slideshow under section "A Tug of War Between the Gods".