The instructional presentation to introduce students to pi

1. Created by Jan Abernethy
March 2006

2. What is Pi?
• Pi is defined as the ratio
of the circumference to
the diameter of a circle
• Pi is usually denoted
with this greek symbol:
π
π =
circumference
diameter

3. 3.141592551104866223558431126381048812355898112276391048823661691
12648104891237105711355110577023712221136511058672371277113652105
86823713861136671058762371496113682105891237171611369410589123723
75113696105806987498576984769847609873409867439857694387569803475
28937465283974658927364587923645897236458723645987236859742365298
76458726345897623897465283746587293465897236458726458972436952384
92322547392938475623987562897465298376598726549872365987236598726
87968197871987261987618719876187632198716239874168971236489761238
97641238976143298761911010101032178648764387263874687638763286234
23189432943213458745984753489760975645784326574365743256743657432
65743256743265743276543265743265743268743268743268743268732468742
38763468727364872364872634872634876238476287346872164872648726348
71623487216348762138746218764318726348712634876123876482173647126
34872163487621387462873647213648271364872136487126348726487126387
62487263847623876418276348716234871623874682734687126348721634872
61873461287364871263487126348761238746128736418732648712648754354
39875438935409453809543805349854309854309801010101029389813287243
87634287643287648723648762384762387462873648726348726348726348726
What is the “Value” of Pi?
• Pi is an irrational number – its decimals repeat forever
• Mathematicians estimate digits of pi to use it in real world
settings. Click here to find digits of pi.
• Pi is usually rounded off to about 3.1415

4. History of Pi
• The hunt for pi began in Egypt and in Babylon
about two thousand years before Christ. The
Egyptians obtained the value (4/3)4 and the
Babylonians the value 3 1/8 for pi. About the
same time, the Indians used the square root of
10 for pi. These approximations to pi had an
error only as from the second decimal place.

5. Who Discovered Pi?
• Archimedes was the first to
theoretically approximate pi
• He calculated that pi was
“trapped” between 223/71 and
22/7, or roughly 3.1428
• Today we use better
approximations, most of
which are derived by
computers
Hi, I’m
Archimedes…
Pi = Between
223/71 and 22/7

6. The Death of Archimedes
Archimedes was born in 287 BC in a Greek
state called Syracuse, Sicily.
The city of Syracuse was taken over by the
Romans and Archimedes was killed.
It is said that he was busy drawing circles in
the dust and writing mathematical equations
at the time of his death
THAT’S HOW IMPORTANT PI
WAS TO ARCHIMEDES!!!!!

7. THE DISCOVERY OF PI
Who? When? Discovery Equivalence
Egyptians 2000 BC (4/3)4
3.160493827...
Babylonians 2000 BC 3 1/8 3.125
Indians 2000 BC
square
root of 10 3.16227766...
Archimedes 250 BC 22/7 3.14128…
Computers Today Pi 3.1415926535…
Currently the value of pi is known to 6.4 billion places!

8. The Usefulness of Pi
• Pi is extremely useful in calculating the area
and circumference of a sphere: A = πr2 and
C = 2πr.
• Many disciplines of science use π in their
equations to describe the world
• In fact DNA, rainbows, the human
eye, music, color, and ripples
all have some natural roots in pi.

10. Diameter and Radius
• The distance across a circle
through its center is called its
diameter, D.
• The radius, R of a circle is the
distance from the center of a
circle to a point on the edge of
the circle.
• So a circle's diameter is twice
as long as its radius: D = 2 × R.
diameter, D
radius, R

11. radius

12. diameter

13. •The distance around a circle is its circumference
diameter
nce
circumfere 


14. π =
circumference
diameter
circumference
2 x radius
π =
Pi = circumference divided by diameter
Every time you use these formulas, you will come up with
3.14159265…

15. area, A
2
area r


•The space inside a circle is called the Area

16. I drew polygons of
more than 90 sides!
Take it from me… the
area of a circle is
πr2

17. APPROXIMATELY
~
=
The symbol means
When speaking of pi we always use ~
=
Example:
π ~
= 3.14

18. LET’S REVIEW THE FORMULAS!
2
area r


π =
circumference
diameter
diameter
nce
circumfere 


19. SOME NAMES FOR PI
3.14
~
= ~
=
22
7
___
pi π
Hope you enjoyed
learning about Pi!!!