a-sketch-of-computer-programming-v-math-variables.js

/*
# A quick sketch of a few ways that variables in computer programming relate to algebraic variables

A common (a la Bednarz, Kieran, & Lee, 1996; Küchemann, 1981; 
MacGregor & Stacey, 1993; Malle, 1993; Usiskin, 1988) breakdown 
of the functions of variable are into:
📭 — placeholder for number
❔ — an unknown number
📈 — a varying quantity
🎁 — a generalized number
📨 — and a parameter

I've annotated the code below with emoji indicating which of the uses above are entailed.
*/

var l; // 📭
l = 5;

//////////
// Find the intersection of two functions discretely

var y1 = (x) => x * x; // 📭, 🎁, 📨
var y2 = (x) => x; // 📭, 🎁, 📨
var find_intersections = function(f1, f2, domain_start, domain_end, epsilon = 0.0001, step_size = 0.01) { // 📭, 🎁, 📨
    intersections = []; // ❔
    x = domain_start; // 📈
    while (x <= domain_end) { // 📈, 🎁
        if (Math.abs(f1(x) - f2(x)) <= epsilon) { // 🎁
            intersections.push(x); // ❔
        }
        x += step_size; // 📈
    }
    return intersections; // 📭
};
console.log(find_intersections(y1, y2, 0, 100));


//////////
// Represent the addition of complex numbers

var Complex = function(real, imaginary) { // 🎁, 📨
    this.real = (typeof real === 'undefined') ? this.real : parseFloat(real); // 📭, ❔
    this.imaginary = (typeof imaginary === 'undefined') ? this.imaginary : parseFloat(imaginary); // 📭, ❔
};
Complex.add = function(c1, c2) { // 🎁, 📨
    return new Complex(c1.real + c2.real, c1.imaginary + c2.imaginary); // 📈, 🎁, 📨
};
var x = new Complex(1, 0); // 📭
var y = new Complex(0, 1); // 📭
console.log(Complex.add(x, y));