Approximate pi by throwing darts

pi_darts.R

library(tibble)
library(ggplot2)

# Imagine a circle inscribed in a unit square
# We can converge (slowly) on the value of pi by throwing random darts
# at this target; counting how many fall in versus out of the circle;
# and using the resulting approximate area ratio to calculate pi.

set.seed(12345)

n_darts <- 1000

darts <- tibble(dart = seq_len(n_darts),
                x = runif(0, 1, n = n_darts), # each dart lands at x,y
                y = runif(0, 1, n = n_darts),
                # if a dart is within 0.5 units of the center, it's "in"
                dist_from_center = sqrt((x - 0.5) ^ 2 + (y - 0.5) ^ 2),
                in_circle = dist_from_center <= 0.5, 
                in_count = cumsum(in_circle),
                # running approximation for pi, based on A = pi r^2
                pi_est = in_count / dart / 0.25)

qplot(dart, pi_est, data =  darts, geom = "line") + geom_hline(yintercept = pi, color = "blue")

# I actually did this one time with a class for real--dropped objects from
# a second floor balcony and counted how many landed in versus out