// Copyright 2013-2018 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// https://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! # Monte Carlo estimation of π
//!
//! Imagine that we have a square with sides of length 2 and a unit circle
//! (radius = 1), both centered at the origin. The areas are:
//!
//! ```text
//! area of circle = πr² = π * r * r = π
//! area of square = 2² = 4
//! ```
//!
//! The circle is entirely within the square, so if we sample many points
//! randomly from the square, roughly π / 4 of them should be inside the circle.
//!
//! We can use the above fact to estimate the value of π: pick many points in
//! the square at random, calculate the fraction that fall within the circle,
//! and multiply this fraction by 4.
extern crate rand;
use ;