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var vertices = [];
function mouseDragged()
{
if (document.getElementById("info").innerHTML != "")
return;
if (mouseX < 0 || mouseX > width || mouseY < 0 || mouseY > width)
return;
stroke(0);
vertices.push([mouseX, mouseY]);
if (vertices.length > 1)
line(mouseX, mouseY, vertices[vertices.length-2][0], vertices[vertices.length-2][1]);
}
function circumference()
{
var total = 0;
for (var i = 1; i < vertices.length; i++)
{
total += dist(vertices[i-1][0], vertices[i-1][1], vertices[i][0], vertices[i][1]);
}
return total;
}
function center()
{
var centerX = 0;
var centerY = 0;
for (var i = 0; i < vertices.length; i++)
{
centerX += vertices[i][0] / vertices.length;
centerY += vertices[i][1] / vertices.length;
}
return [centerX, centerY];
}
function twoPiApprox()
{
var o = center();
var c = circumference();
ellipseMode(CENTER);
fill(0, 0, 200);
noStroke();
ellipse(o[0], o[1], 5, 5);
var avgR = 0;
var minLocation;
var maxLocation;
for (var i = 0; i < vertices.length; i++)
{
var d = dist(vertices[i][0], vertices[i][1], o[0], o[1]);
avgR += d / vertices.length;
}
stroke(0, 255, 0);
noFill();
line(o[0], o[1], o[0]+avgR, o[1]);
stroke(255, 0, 0);
ellipse(o[0], o[1], 2*avgR, 2*avgR);
stroke(255, 200, 0);
ellipse(o[0], o[1], c/PI, c/PI);
return c/(2*avgR);
}
function setup()
{
createCanvas(500, 500);
stroke(255, 0, 0);
line(0, 0, width-1, 0);
line(width-1, 0, width-1, height-1);
line(0, height-1, width-1, height-1);
line(0, 0, 0, height-1);
}
function calculate()
{
var approx = twoPiApprox();
var avgPi = approx;
var percentError;
if (avgPi > PI)
{
percentError = 100*(avgPi/PI - 1);
}
else
{
percentError = 100*(PI/avgPi - 1);
}
var div = document.getElementById("info");
div.innerHTML = "Your approximation | True value<br> 2π = " + 2 * avgPi + " | " + TWO_PI + "<br> π = " +
+ avgPi + " | " + PI + ".<br>" + percentError + "% error.<br>"
+ "The blue dot is the center of your shape. The green line is the average radius of the shape.<br>"
+ "The red circle is a circle with the same radius as your shape, and the orange circle is a<br>"
+ "circle with the same circumference as your shape. The closer they are, the better your<br>"
+ "approximation of π";
}
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