You have been given a circular object. Use a tape measure, and accurately measure the diameter and the circumference of your object to the nearest tenth of a centimeter. If you do not have a tape measure, use a piece of string and a ruler to determine the measurements.
DIVIDE THE CIRCUMFERENCE BY THE DIAMETER_______________________________
Write the results of your findings on the board, and complete the chart below showing the class results.
DIAMETER CIRCUMFERENCE QUOTIENT
Find the mean value for the classes quotients ______________________________________
Pi Around the World
Find the values for pi that the following groups or individuals discovered.
1. Close to 4000 years ago, the ancient Babylonians figured pi at 25/8. Divide 25 by 8. __________________
2. Ancient Egyptians wrote pi as 256/81. Divide 256 by 81. __________________
3. Here's a puzzle from the Bible. The Old Testament recounts that King Solomon created a "molten sea," a sort of ceremonial pool for his temple. The pool was splendid with 12 brass oxen surrounding it. The sea measured 10 cubits from one brim to the other, which was the diameter. A line of 30 cubits "did compass it round about" which was the circumference. So, divide 30 by 10 to estimate King Solomon's value for pi.
4. The Greek mathematician Archimedes said that pi was more than 3 10/71 but less than 3 1/7. Change both mixed numbers to decimals.
5. The Chinese people of the fifth century calculated pi as 355/113. Find the decimal equivalent.
6. Aryabhata was a mathematician in India about 1500 years ago. His value was 62,832 divided by 20,000. Divide to see how close he was.
7. Bhaskara was a mathematician of India in about the year 1150. He calculated the value of pi as the square root of 10. Use the square root key to find his value.
8. Use your calculator's pi key to find the value that it uses for pi. _____________________Which group or person had the best number to use for pi? ____________________________
Which group was the worst? _______________________
Whose value do we use today, as the best fraction for pi? _____________________________
Why do you think that people in history used fractions, and not decimals,
when they needed a numerical value for pi?
Buffoon's Toothpick Experiment
Cut four 1-centimeter pieces from toothpicks. From a reasonable height, randomly drop the four sticks onto the ruled surface below. A "hit" occurs when a stick lands on or across one of the lines. Count the number of hits on each of 25 drops of the four sticks. Keep an accurate record below.
Number of hits each drop. __________________________________________________________
Total number of hits. ______________________________________________________________
Divide the total number of sticks dropped (100) by the number of hits. What is the quotient? ___________________
Add your results to the class results. Determine the class total for drops and hits. Find the quotient of these two numbers.