Bertrand's Experiment

Bertrand's experiment is to generate a random chord of a circle. In the simulation, one point of the chord is fixed at (1, 0) and the other random point (X, Y) is recorded on each update in the first table. Also recorded are D, the length of the line segment from the center of the circle to the center of the chord, and A, the angle that this line segment makes with the horizontal. Variable I indicates the event that the chord is longer than the length of a side of the inscribed equilateral triangle. The density of I is shown in blue in the distribution graph and and is recorded in the distribution table. On each update, the empirical density of I is shown in red in the distribution graph graph and is recorded in the distribution table. Either of two models can be selected with the list box: the model where the distance D is uniformly distributed, and the model where the angle A is uniformly distributed.