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 // Copyright 2018 Developers of the Rand project. // Copyright 2013-2018 The Rust Project Developers. // // Licensed under the Apache License, Version 2.0 or the MIT license // , 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. #![cfg(feature = "std")] use rand::distributions::{Distribution, Uniform}; fn main() { let range = Uniform::new(-1.0f64, 1.0); let mut rng = rand::thread_rng(); let total = 1_000_000; let mut in_circle = 0; for _ in 0..total { let a = range.sample(&mut rng); let b = range.sample(&mut rng); if a * a + b * b <= 1.0 { in_circle += 1; } } // prints something close to 3.14159... println!( "π is approximately {}", 4. * (in_circle as f64) / (total as f64) ); }