Calculating Pi (Version 2)
He Was Born More Than 2000 Years Ago, But I Bet He's Smarter Than You!
Archimedes is a famous scientist who was born over 2000 years ago. Among his many contributions to the world was finding a way calculate the value of pi to a high level of precision. Using this method, he was able to determine that the value is between 3.1429 to 3.1408. That's pretty impressive since calculators weren't invented yet!
Archimedes Statue In Berlin Germany
What Is Pi
Pi is denoted with the Greek symbol . It is the defined as the ratio between a circles circumference to it's diameter. I.E. It is a very useful number and is used to calculate the area of a circle and surface area and volume of a sphere. It is also used to measure angles in radians. Pi is used in all sorts of jobs including by scientists, engineers, programmers, mathematicians and even school teachers.
Defining Pi
How Did He Do It
The challenge that Archimedes faced was that there wasn't a way to directly calculate the circumference of a circle. You may think that drawing a circle and using a string to measure it's circumference would be a good solution, however that would not have been accurate enough. What he did know how to do however was to calculate the perimeter of a polygon. See if you can figure out how he used this knowledge to calculate pi. Look at the interactive circle below and see if you can also figure it out!
Pssstt.. we know now that pi = 3.14159265358979323846264338327950288419716939937510.......
Calculate
Response Time
In the space below, describe how you think Archimedes calculated pi? Does the size of the circle effect the calculations? Do you think there could have been a better way for someone to calculate pi before calculators were invented?
Extension
So that was the technique, but how did he actually calculate the perimeter of the polygons? Watch the below video to find out!