Shortly you will see students doing research on pi. They rolled the bike along the pavement. They measured distance rolled for 5 revolutions in a straight line. Divided that distance by 5. Measured the radius/diameter of the wheel. Divided the distance of one revolution (Circumference) by radius.
What number do you think they got?
Why do you suppose they made 5 revolutions?
How did they get the distance rolled in one revolution?
What would happen if a smaller wheel was used?
What suggestions can you think of that will increase their accuracy?
What is the difference between accuracy and precision?
The early Babylonians and Hebrews used three as a value for Pi. Later, Ahmes, an Egyptian found the area of a circle . Down through the ages, countless people have puzzled over this same question, “What is Pi?"
From 287 - 212B.C. there
lived Archimedes, who inscribed
in a circle and circumscribed
about a circle, regular polygons.
The Greeks found Pi to be related to
cones, ellipses, cylinders and other
Circumscribe polygons about a circle and inscribe polygons in a circle. Circumscribed polygons Inscribed polygons
Measure the perimeter of each polygon and make a table. Notice the differences decrease as the number of sides increase. Using this method, Pi was found to be between 3 1/7 and 3 10/71.
During the 17th century, analytic geometry and calculus were developed. They had a immediate effect on Pi. Pi was freed from the circle! An ellipse has a formula for its area which involves Pi (a fact known by the Greeks); but this is also true of the sphere, cycloid arc, hypoclycloid, the witch, and many other curves.
Around 1950, Borel noted that numbers like the Square Roots of
2, 3, etc. appear to be a mere jumble of digits, but on the
average each digit appears a fixed fraction of the
time. (Some people say this is characteristic of a random set
of numbers. Do the digits of Pi occur randomly?)
Such number are called 'normal.' With computers widely
available the race was on again!
1950 Eniac in 70 hours produced 2,036 digits
1954 More in 13 minutes produced 3,093 digits
1959 IBM 708 in 1 hr 40 min produced 10,000 digits
1959 Pegasus produced > 100,000 digits
As said in the beginning, “There is more to Pi than meets the eye
The computation of Pi to 10,000 places may be of no direct scientific usefulness. However, its usefulness in training personnel to use computers and to test such machines appears to be extremely important. Thus the mysterious and wonderful Pi is reduced to a gargle that helps computing machines clear their throats.