According to Google Maps, the area of the state of Texas is 268,820 square miles. Texas almost fits into a square! The North to South distance is 765 miles and the East to west distance is 775 miles.The area of the rectangle formed by these two distances is 592,875 square miles. The image of Texas is drawn to the same scale as the rectangle. SET THE NUMBER OF POINTS TO BE RANDOMLY SELECTED IN THE RECTANGLE IN THE THROWS SLIDER, CLICK ON THE GREEN FLAG, AND COMPARE THE MONTE CARLO APPROXIMATION TO THE 268,820 SQUARE MILES AREA OF TEXAS.
I introduced the Monte Carlo method in my Scratch project http://scratch.mit.edu/projects/16816029/ Monte Carlo Simulation of Pi. This project demonstrates that the Monte Carlo method when used to approximate the area of a shape can be applied to very irregular shapes. To approximate the area of any irregular two-dimensional shape, simply place it in a rectangle of known dimensions, select a number of random points, count the number in the shape, and then compute the ratio of the number in the shape to the area of the rectangle. The number 268, 820 square miles is itself an approximation. Where did Google get that number?
