The true value of Pi to 8 decimal digits is 3.141592654 so this means Archimedes got it correct to two decimal places - and 3.14 is even today the figure given to school children to use in math book problems.Īrchimedes' approach was to draw a regular polygon inside the circle and another outside it. Using decimal notation and rounding to 8 decimal places, this means Pi is between 3.14084507 and 3.142857143. The formulas they used for the area of circle indicate the equivalent value for π as 377/120, 3 1/8, or 256/81.Īrchimedes found out that this ratio was between 3 10/71 and 3 1/7. Ancient cultures were aware of the fact that the ratio of any circle's circumference to diameter was a constant. Mathematicians didn't find find out about all that for thousands of years. AND without ever settling into any pattern! This is something quite amazinga and puzzling! Being an irrational number means that if you write π as a decimal, its decimal digits go on forever. In reality, π is not any fraction or a simple decimal, but an irrational number – one that you cannot write as a fraction using two whole numbers.
Hopefully at least some of them will get their average ratio as being between 3.1 and 3.2. They should calculate the average of the ratios they get. Students will naturally get varying results because it's impossible to measure totally accurately. This is a great hands-on activity and a starting point for a discussion about Pi! Students can easily find out this ratio on their own by MEASURING the circumference (with a measuring tape) and the diameter (with a ruler) of several circles, and then calculating the ratio of them.
The definition of Pi says it is the ratio of any circle's circumference to its diameter.