Overview The Quincunx Board, also called the Galton Board, was named after Sir Francis Galton. This structure consists of a triangular array of pegs. Small balls, according to the space left between consecutive pegs, are dropped onto the top peg. These balls bounce their way down and move either towards the right or left on hitting a peg. At the bottom, they are collected in small bins. But it is interesting to note that if there is an equal chance of bouncing left or right, most of the balls tend to fall in the bins towards the middle. If the graph of the data is made, then the ‘bell-shaped’ curve of normal distribution can be seen.
Objectives The aim of our project is to make a Quincunx board and visualize the curve of normal distribution. We will see what happens when we pass 100 balls through the quincunx board.
Materials Required <ul><li>To make a Quincunx Board, we require the following material </li></ul><ul><li>Plywood </li></ul><ul><li>Enamel Paints </li></ul><ul><li>Nails and Hammer </li></ul><ul><li>Cardboard and Covering paper </li></ul><ul><li>Geometry box </li></ul><ul><li>Marbles </li></ul>
Procedure Day-1 STEP 1: Firstly, take the piece of plywood and paint it.
STEP 2: After it dries, draw the lines and dots on which you want to fix the nails…… …… so that it looks like this. Day-2
STEP 3: Fix nails into the board at the marked points. Then cut the plywood. STEP 4: Paint numbers from 1 to 11 under the spaces between the nails in the bottom row.
STEP 5: Make a bin using cardboard and cover it. The bin should be big enough to keep the board in it. Now it’s ready!
STEP 6: Drop 100 balls on top of the board and record how many balls fall through specific spaces. Then draw the graph of your observations.
Observations On dropping 100 marbles through the Quincunx board, these were my observations- 0 1 8 10 22 27 11 15 4 0 2 No. of balls 11 10 9 8 7 6 5 4 3 2 1 Slot No.
This is how the graph of the data looks like- We can get even better results by using more marbles. The two curves look somewhat similar. Curve of Normal Distribution
Result We saw that most of the balls ended up in the middle bins. So, after performing this activity, we can conclude that in a quincunx board, if all the balls have an equal chance of bouncing left or right, a large proportion of them will fall in the center and we will be able to see a skewed version of the curve of normal distribution.
Extension You can take a look at Pascal's Triangle. In fact, the Quincunx is just like Pascal's Triangle, with pegs instead of numbers. The number on each peg shows you how many different paths can be taken to get to that peg. Amazing but true. Quincunx Board Pascal’s triangle
I have picked up some of the information for my presentation from the following sites- http://www.mathsisfun.com http://www.wikipedia.org References
Acknowledgements I would like to thank my math teacher, Ms. Rashmi Kathuria for motivating me and giving me the guidelines for this project, and also my father for clicking the pictures.