*  Calculate an approximation of pi by

*  increasing the sides of a regular polygon.

*  P/(2*apothem) is approx pi

*  On pi/2021

*  by @ajuancer (juancer.me)

*/

​

let sideL = 60; // Side length.

let sideNo = 3; // no of sides

// With sideL = 1 and sideNo =10 000, the obtained value of

// pi is 3.1415926(...)

​

function setup() {

  createCanvas(900, 900);

  rectMode(CENTER);

​

  let button = createButton("Show info");

  button.position(30, 150);

​

  button.mousePressed(() => {

    if (document.getElementById("intro").style.display == "none") {

      document.getElementById("intro").style.display = "block";

      button.elt.innerText = "Hide info";

    } else {

      document.getElementById("intro").style.display = "none";

      button.elt.innerText = "Show info";

    }

  });

}

​

function draw() {

  background(220);

  push();

  translate(width / 2, height / 2);

​

  [ap, per, iAngle] = polygon(0, 0, sideL, sideNo);

​

  textSize(20);

  text(`Perimeter: ${per}`, -width / 2 + 32, -height / 2 + 32);

  text(

    `Apothem (approx): ${round(ap, 5)}`,

    -width / 2 + 32,

    -height / 2 + 32 * 2

  );

  text(

    `Interior angle (approx): ${round(iAngle, 5)}`,

    -width / 2 + 32,

    -height / 2 + 32 * 3

  );

​

  // Get pi

  calcPi = sideNo * sin(iAngle / 2);

​

  // Compare results.

  fixedDecimals = {};

  strCalcPi = calcPi.toString();

  const PI_STRING = PI.toString();

  for (i = 1; i < 14; i++) {

    if (

      strCalcPi.substring(0, i).localeCompare(PI_STRING.substring(0, i)) != 0

    ) {

      fixedDecimals.common = strCalcPi.substring(0, i - 1);

      fixedDecimals.diff = strCalcPi.substring(i);

      break;

    }

  }

​

  // Write pi

  text("Calculated PI:", -width / 2 + 32, -height / 2 + 32 * 4);

  fill(33, 203, 103);

  text(

    fixedDecimals.common,

    -width / 2 + 32 + textWidth("Calculated PI: "),

    -height / 2 + 32 * 4

  );

  fill(258, 51, 51);

  text(

    fixedDecimals.diff,

    -width / 2 +

      32 +

      textWidth("Calculated PI: ") +

      textWidth(fixedDecimals.common),

    -height / 2 + 32 * 4

  );

  fill(255, 255, 255);

  pop();

  frameRate(10)

  if (sideNo < 100) {

    sideNo++;

    sideL *= 0.99999

  } else if (sideNo<300){

    sideNo++;

    sideL *= 0.995

  }

}

​

// Based on polygon() of

// www.p5js.org/examples/form-regular-polygon.html

function polygon(x, y, side, npoints) {

  let angle = TWO_PI / npoints;

  let radius = side / (2 * sin(angle));

  beginShape(TRIANGLE_FAN);

  vertex(0, 0);

  for (let a = 0; a < TWO_PI + angle; a += angle) {

    let sx = x + cos(a) * radius;

    let sy = y + sin(a) * radius;

    vertex(sx, sy);

  }

  endShape(CLOSE);

  let ap = side / (tan(angle / 2) * 2);

  return [ap, npoints * side, angle];

}

​