The document discusses the history of pi. [1] Ancient cultures like the Babylonians, Egyptians, Chinese, and Hebrews approximated pi to be between 3 and 3 1/8. [2] In ancient Greece, Euclid proved that the ratio of a circle's circumference to its diameter is always the same, and Archimedes discovered pi to be approximately 22/7. [3] The document provides instructions for students to calculate the circumference, area, and volume of geometric shapes using pi.

1. The Mysteries of Pi
by Taylor and Aarambh

2. Pi’s Early History
Different cultures had different values.
The Ancient Babylonians used 3 1/8 for
their value of pi by taking 3 times the
square of a circles radius which was 3 1/8.
The Egyptians used (16/9)2
The Chinese said pi was 3.
The Hebrews said pi was 3 also, based on
what they learned in the bible.

3. More of Pi’s History
In Egypt in the 400’s B.C, a mathematician named Euclid
proved that the ratio of the circumference to the diameter
of a circle is always the same.
Archimedes studied in Alexandria. He discovered the value of
pi to be about 22/7 We still use this approximation today.
.
Archimedes’s method for approximating pi: The
area of the circle is in the areas of the
circumscribed and the inscribed hexagons.

4. Calculating Pi
To calculate an approximate value of pi,
measure the diameter and the
circumference of a circle (using a piece of
string perhaps). Divide the circumference
of the circle by the diameter. Keep in mind:
This is an approximation.

5. Class Activity: #1
!
! !
"#$%!
Calculate the circumference – C – of the circle above using
one of the following equations:
C=2πr or C=πd
r=radius d=diameter

6. #2
!
! !
"#$%!
Calculate the area – A – of the circle above using one of the
following equations:
A=πr2 or A=πd2/ 4
r=radius d=diameter

7. #3
! !
!
"#$%&! !
!
"#$%&!
Calculate the volume – V – of the cylinder above using one of
the following equations:
V=πr2h or V=πd2/ 4h
r=radius d=diameter h=height

8. Answers: #1
C = 2πr
C = 2 x 3.14 x 3
C = 18.84 inches
OR
C = πd
C = 3.14 x 6
C = 18.84 inches

9. #2
A = πr2
A = 3.14 x r x r
A = 3.14 x 3 x 3
A = 28.26 inches
OR
A = πd2/4
A = 3.14 x d x d /4
A = 3.14 x 6 x 6 / 4
A = 28.26 sq. inches

10. #3
V = πr 2 x h
V= 3.14 x 10 x 10 x 30
V = 9420 cubic inches

11. Bibliography
The Amazing History of Pi. 23 Apr. 2010. <http://ualr.edu/
lasmoller/pi.html>.
The Everlasting Pi. 29 Apr. 2010. <http://abishek.webs.com/
usesofpi.htm>.