Illustrations for the proof of Green's theorem / Mark McClure

I'm a professor of mathematics at the University of North Carolina Asheville. I've also done a fair amount of consulting work over the years focusing on scientific and data visualization. I'm happy to be part of the first Observable Ambassador's cohort.

Workspace

Public

Edited

Sep 30, 2024

pts = {

new_curve;

new_curve2;

let n = 150;

let [a, b] = [1, 2].map(d3.randomUniform(1, 5));

let [p, q] = [1, 2].map(d3.randomUniform(0.1, 0.9));

let theta = d3.randomUniform(0, 2 * Math.PI)();

let cos_theta = Math.cos(theta);

let sin_theta = Math.sin(theta);

let R = (x, y) => [

cos_theta * x - sin_theta * y,

sin_theta * x + cos_theta * y

];

let skew = d3.randomUniform(0, 0.5)();

function r(t) {

let c = Math.cos(t);

let s = Math.sin(t);

let x = (1 - c * skew) * a * Math.sign(c) * Math.abs(c) ** p;

let y = b * Math.sign(s) * Math.abs(s) ** q;

let [X, Y] = R(x, y);

return [X, Y];

}

let pts = d3.range(0, 2 * Math.PI + Math.PI, Math.PI / n).map(r);

pts.rot = -((180 * theta) / Math.PI + 90);

let [xmin, xmax] = d3.extent(pts.map((pt) => pt[0]));

let [ymin, ymax] = d3.extent(pts.map((pt) => pt[1]));

pts.xmin = xmin;

pts.ymin = ymin;

pts.xmax = xmax;

pts.ymax = ymax;

pts.size = Math.ceil(d3.max([xmax, -xmin, ymax, -ymin]));

return pts;

}

pc = require("polygon-clipping")

MathJax = require("https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js").catch(

() => window["MathJax"]

)

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