absolute-value-of-vectors.js

/**
 * Originally created in JS Bin: http://jsbin.com/yetubi/edit?js,console
 * Dependencies: lodash
 * 
 * This script finds 4 whole number values that have a specific relationship.
 * Specifically, the sum of the squares of 3 numbers when they equal the
 * square root of the 4th number. In linear algebra terms, this calculates
 * the absolute value of a vector [x, y, z] when all values and the result
 * are whole numbers. This formula is also known to calculate the distance
 * of a 3D point from zero: d = sqrt(x*x + y*y + z*z)
 *
 * I recognize it's totally silly, but I wrote this because I was writing a
 * unit test for a function that performs this calculation and I wanted my
 * test cases to be whole numbers. This script is how I found them. I also
 * thought this was a great little code kata in writing an algorithm.
 *
 * skip controls the smallest value in the vector
 * start and stop control the range of distance, d
*/

console.clear()

const skip = 2
const start = 9
const stop = 100

var getNext = (arr, target, result) => {
  if(arr.length === 0) return result
  const current = _.last(arr)
  result.push(current)
  const next = target - current
  const slice = _.filter(arr, (i) => { return i <= next })
  return getNext(slice, next, result)
}

var getAnswer = (num) => {
  const target = Math.pow(num, 2)
  const square = (val) => { return Math.pow(val, 2) }
  const squares = _.range(skip, num).map(square)
  const maybe = getNext(squares, target, [])
  const check = _.reduce(maybe, (total, i) => total + i)
  if(maybe.length === 3 && check === target) {
    console.log(num + ': '+ _.map(maybe, Math.sqrt))
  }
}

_.range(start, stop).map(getAnswer)