Measurements Of Polygons And Circles Worksheets - Lance Mangham, 6th Grade Math, Carroll Isd Page 23
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40Activity 10-18: Extraordinary Pi
Name:
• Pi is the number of times a circle’s diameter will fit around its circumference.
• Here is pi to 64 places:
3.1415926535897932384626433832795028841971693993751058209749445923
• Pi occurs in hundreds of equations in many sciences including describing DNA, a rainbow,
ripples where a raindrop fell into water, distribution of prime numbers, geometry problems,
waves, navigation, etc.
• Half the circumference of a circle with radius 1 is exactly Pi. The area inside that circle is also
exactly Pi!
• Taking the first 6,000,000,000 decimal places of Pi, this is the distribution:
0 occurs 599,963,005 times
1 occurs 600,033,260 times
2 occurs 599,999,169 times
3 occurs 600,000,243 times
4 occurs 599,957,439 times
5 occurs 600,017,176 times
6 occurs 600,016,588 times
7 occurs 600,009,044 times
8 occurs 599,987,038 times
9 occurs 600,017,038 times
• Pi is irrational. An irrational number is a number that cannot be expressed in the form (a / b)
where a and b are integers.
• The Babylonians found the first known value for Pi in around 2000BC; they used (25/8) The
Egyptians used Pi = 3 but improved this to (22 / 7). They also used (256/81).
• In around 200 BC Archimedes found that Pi was between (223 / 71) and (22 / 7). His error was
no more than 0.008227%. He did this by approximating a circle as a 96 sided polygon.
• Ludolph Van Ceulen (1540 - 1610) spent most of his life working out Pi to 35 decimal places. Pi
is sometimes known as Ludolph's Constant.
• The first person to use the Greek letter was Welshman William Jones in 1706. He used it as an
abbreviation for the 'periphery' of a circle with unit diameter.
• The Pi memory champion is Hiroyoki Gotu (21 years old) who memorized an amazing 42,000
digits.
• Pi was calculated to 2,260,321,363 decimal places in 1991 by the Chudnovsky brothers in New
York.
• Most people would say that a circle has no corners - but it is more accurate to say that it has an
infinite number of corners.
• At position 762 there are six nines in a row. This is known as the Feynman Point.
th
Created by Lance Mangham, 6
grade math, Carroll ISD
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