Buffon's Coin Problem
Georges-Louis Leclerc, Comte de Buffon (1707 – 1788) was a french mathematician and naturalist. He began the study of
geometric probability with his coin and needle problems. Geometric probabilities are computed by the comparison of measurements.
Geometric Probability involves the comparison of measurements to compute probabilities.
Toss a coin at the grid. What is the probability that the coin does not cross a grid line? How does that probability change if you change the
size or shape of the grid? or the size of the coin?
- Use the 'Toss once' and 'Toss 100 times' buttons to toss the coin at the grid. Note that the coin will land completely within the grid;
it will not cross the outside border.
- When the coin lands, the center is either orange or blue.
- An orange center indicates that the coin crossed a grid line.
- The blue center indicates that the coin did not cross a grid line.
- A running count of the number of tosses and the number of successes (the coin lands without crossing any lines) is displayed on the
right panel of the applet.
- When the coin is tossed multiple times, outlines indicating where the coin landed on previous tosses are displayed.
- When the 'Show Centers Only' checkbox is selected, the center marks, again either blue or
orange, of previous tosses are displayed rather than the full outlines.
The size of the grid divisions and the shape of the grid can be changed. To change the shape of the grid, choose 'Change Grid' from
the 'Display Menu'. Then select from:
Use the spinners at the top of the right panel to adjust the height and width of the divisions in the grid.
- A rectangular grid.
- A Grid of diamonds.
- Horizontal lines.
- Vertical lines.
Coin Size: The spinner at the bottom of the applet indicates the diameter of the coin in pixels. Note that the
diameter of the coin can exceed the dimensions of the grid.
Display Menu: The display menu allows the user
- to change animate the coin tosses and modify the speed of the animation
- to change the size of the center markings
- to change the shape of the grid. (See 'Grid' above).