Estimate Pi by Tossing Objects - Count Data
by: Alan R (over 3 years ago)



Project #493

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Description

This iSENSE project is based on a geometrical probability theory developed in the 18th century by French philosopher Georges-Louis Leclerc, Comte de Buffon. He determined that you can estimate the value of pi by dropping straight objects (e.g. toothpicks, craft sticks, or pencils) on a grid of parallel lines separated by a distance equal to the length of the objects thrown. The proportion of sticks crossing a line is directly related to the value of pi, as follows:

pi = (2 x the number of objects thrown) / (the number of objects crossing lines)

The more tosses that are recorded, the more accurate the estimation of pi should become, so please feel free to conduct the activity and record your data!

To produce an estimate of pi based on all data submitted to date, make a bar chart, group by Combined Datasets, display both Number Thrown and Number Crossing Lines on the Y-Axis, set the Analysis Type to Total for each bar, and enter the values into the formula above.

The attached worksheet presents a grid of lines spaced 2.5 inches apart. This is intended to be used as a landing area for standard 2.5-inch toothpicks. (As long as the tossed objects are straight, and as long as the spacing between the lines is equal to the length of the object, it doesn't matter what objects are used.)

The attached worksheet is based on an activity presented here:
http://www.sciencefriday.com/blogs/03/12/2014/estimate-pi-by-dropping-sticks.html

Another description of the activity (using hotdogs) can be found here:
http://www.wikihow.com/Calculate-Pi-by-Throwing-Frozen-Hot-Dogs

Fields
Name Units Type
Number Thrown
Objects
Number
Number Crossing Lines
Objects
Number
Formula Fields
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Media
File Name
Tn toothpick

Estimate Pi by Tossing Objects - Count Data

Project #493 on iSENSEProject.org


Description

This iSENSE project is based on a geometrical probability theory developed in the 18th century by French philosopher Georges-Louis Leclerc, Comte de Buffon. He determined that you can estimate the value of pi by dropping straight objects (e.g. toothpicks, craft sticks, or pencils) on a grid of parallel lines separated by a distance equal to the length of the objects thrown. The proportion of sticks crossing a line is directly related to the value of pi, as follows:

pi = (2 x the number of objects thrown) / (the number of objects crossing lines)

The more tosses that are recorded, the more accurate the estimation of pi should become, so please feel free to conduct the activity and record your data!

To produce an estimate of pi based on all data submitted to date, make a bar chart, group by Combined Datasets, display both Number Thrown and Number Crossing Lines on the Y-Axis, set the Analysis Type to Total for each bar, and enter the values into the formula above.

The attached worksheet presents a grid of lines spaced 2.5 inches apart. This is intended to be used as a landing area for standard 2.5-inch toothpicks. (As long as the tossed objects are straight, and as long as the spacing between the lines is equal to the length of the object, it doesn't matter what objects are used.)

The attached worksheet is based on an activity presented here:
http://www.sciencefriday.com/blogs/03/12/2014/estimate-pi-by-dropping-sticks.html

Another description of the activity (using hotdogs) can be found here:
http://www.wikihow.com/Calculate-Pi-by-Throwing-Frozen-Hot-Dogs


Fields
Name Units Type of Data
Number Thrown
Objects
Number
Number Crossing Lines
Objects
Number

Our Data
Name(s): ______________________________________
Date: _________________________________________

Number Thrown Number Crossing Lines