Transcript Easy As A Pi - stupidchicken comic

Lesson Objectives
1. You will gain a deeper understanding of the
fundamental concept of pi.
2. You will discover that there is a special relationship
between circumference and the diameter of a circle.
3. You will discover the approximate value of pi.
4. You will understand how the number 3.14 for pi was
determined.
5. You will write a paragraph explaining what pi is.
EASY AS A Pi
Developed by
Ivan Seneviratne
The History of Pi
The importance of pi has been recognized for at least
4,000 years. We know that the Egyptians and the Babylonians
knew about the existence of the constant ratio pi, although they
didn't know its value nearly as well as we do today. They had
figured out that it was a little bigger than 3.
Discovering Pi
1. Draw two circles of different sizes.
2. Measure the circumference and the diameter of the two
circles with a piece of string and ruler.
3. Write down the respective values in a table that has the 3
columns, distance around , distance across middle and
mystery ratio.
4. Demonstrate that by dividing the circumference of an circle
by its diameter you end up with pi.
5. Write your conclusions.
Archimedes' Approximation of Pi
The first mathematician to
calculate pi with reasonable
accuracy was Archimedes. He wrote
a book called “The Measurement of
a Circle” around 250 B.C. stating
that Pi is a number between
3 10/71 and 3 1/7.
The
method
involves
approximating pi by the perimeters
of polygons of 12, 24, 48, and finally
96 sides inscribed
and circumscribed
about a given circle.
Archimedes
(287-212 BC)
The Pi Symbol
The modern symbol for pi
was first used in “Our Modern
Sense” in 1706 by William Jones, a
Welsh mathematics teacher.
Pi, the 16th letter in the
Greek alphabet, was chosen as the
letter to represent the number
3.141592... because the letter pi in
Greek, pronounced like our letter
'p', stands for 'perimeter'.
William Jones
(1675–1749)
Pi Piece of Pi
In 1768, Johann Lambert proved that
Pi is an Irrational number. It means that the
digitsneverendorrepeatinanyknownway.
Today, The most decimal places to
which pi has been calculated is
1,241,100,000,000 (1.2411 trillion digits)
decimal places by Yasumasa Kanada and
Yoshiaki Tamura of The university of Tokyo,
Japan on 20th October 2005 using a HITACHI
SR8000/MPP Super Computer.
Johann Lambert
(1728-1777)
The Pi
Pi is a name given to the ratio of the circumference of
a circle to its diameter.
For the sake of usefulness people often need to
approximate pi. The fraction 22 / 7 is a well used number for
Pi.
When a circle's diameter is 1, its circumference is π.
π = 3.14…
The Many Uses of Pi
 Calculate circumference
 calculate the area of a circle
 The volume of a cylinder
 Describe the DNA double helix
 Calculate field strength
 Calculation of time period in Simple Harmonic Motion
 Determining the distribution of primes
 Analyzing the ripples on water
 In Cryptography
Acknowledgments
 Images
www.acceleratingfuture.com
www.maths.manchester.ac.uk
www.mathematik.de
www.daviddarling.info/encyclopedia
This presentation is developed by Ivan Seneviratne © 2007
purely for personal use.
[email protected]