Question

As we’ve seen, Math is a grab-bag of number-related utility functions, such as Math.max (maximum), Math.min (minimum), and Math.sqrt (square root).

The Math object is used simply as a container to group a bunch of related functionality. There is only one Math object, and it is almost never useful as a value. Rather, it provides a namespace so that all these functions and values do not have to be global variables.

Having too many global variables “pollutes” the namespace. The more names that have been taken, the more likely you are to accidentally overwrite the value of some variable. For example, it’s not unlikely that you’ll want to name something max in one of your programs. Since JavaScript’s built-in max function is tucked safely inside the Math object, we don’t have to worry about overwriting it.

Many languages will stop you, or at least warn you, when you are defining a variable with a name that is already taken. JavaScript does neither, so be careful.

Back to the Math object. If you need to do trigonometry, Math can help. It contains cos (cosine), sin (sine), and tan (tangent), as well as their inverse functions, acos , asin , and atan , respectively. The number π (pi)—or at least the closest approximation that fits in a JavaScript number—is available as Math.PI . (There is an old programming tradition of writing the names of constant values in all caps.)

function randomPointOnCircle(radius) {
  var angle = Math.random() * 2 * Math.PI;
  return {x: radius * Math.cos(angle),
          y: radius * Math.sin(angle)};
}
console.log(randomPointOnCircle(2));
// → {x: 0.3667, y: 1.966}

If sines and cosines are not something you are very familiar with, don’t worry. When they are used in this book, in Chapter 13 , I’ll explain them.

The previous example uses Math.random . This is a function that returns a new pseudorandom number between zero (inclusive) and one (exclusive) every time you call it.

console.log(Math.random());
// → 0.36993729369714856
console.log(Math.random());
// → 0.727367032552138
console.log(Math.random());
// → 0.40180766698904335

Though computers are deterministic machines—they always react the same way if given the same input—it is possible to have them produce numbers that appear random. To do this, the machine keeps a number (or a bunch of numbers) in its internal state. Then, every time a random number is requested, it performs some complicated deterministic computations on this internal state and returns part of the result of those computations. The machine also uses the outcome to change its own internal state so that the next “random” number produced will be different.

If we want a whole random number instead of a fractional one, we can use Math.floor (which rounds down to the nearest whole number) on the result of Math.random .

console.log(Math.floor(Math.random() * 10));
// → 2

Multiplying the random number by 10 gives us a number greater than or equal to zero, and below 10. Since Math.floor rounds down, this expression will produce, with equal chance, any number from 0 through 9.

There are also the functions Math.ceil (for “ceiling”, which rounds up to a whole number) and Math.round (to the nearest whole number).

This is a book about getting computers to do what you want them to do. Computers are about as common as screwdrivers today, but they contain a lot more hidden complexity and thus are harder to operate and understand. To many, they remain alien, slightly threatening things.