Labs / Mathematics
Galton Board
Each ball takes a fresh coin flip at every peg — left or right — and lands in a bin counting how many times it went right. One ball is unpredictable, but pour hundreds and their bell-shaped pile is startlingly regular: the binomial distribution converging on the normal curve. Press and hold on the board to pour a stream.
balls 0μ — · pred 6.00σ — · pred 1.73
What to try
- With a fair board, why does the middle bin fill fastest while the edges stay nearly empty?
- Nudge the bias toward the right. Which way does the whole pile slide, and does its width change too?
- Add more rows. Do the measured mean μ and spread σ track the predicted values more closely or less?
- Only a handful of balls have fallen — how ragged is the histogram, and how many does it take to lock onto the curve?
- Which bias makes the pile widest? What value of p pushes σ to its largest?