Say Hi to Pi
Katherine Carroll
Rationale
 Due to curiosity regarding the origin and
discovery of pi, research was conducted.
 Boy to girl ratio in the Math Category of the
Science Fair.
Applications of Pi
 Class room uses
 Physics and aerospace technology
 Global Paths and Positioning
 Probability
The Life of Pi
 Evolution of pi from the Egyptians to Archimedes
to Srinivasa Ramanujans
 Various methods to calculate pi:
 Calculator Programs
 Creating a Formula
 Buffon’s Needle Experiment
Procedure One
 Three programs were added to calculator.
 Then, the number n was found that estimated pi
accurately to the eighth decimal place.
Programs
Program Two
Program Three
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10
Procedure Two
 A formula was created by using the following method.
 The formula (s2n =
)
and how it changed as the number
of sides increased was understood.
 This formula was used to find a five sided figure inscribed in
a circle with the radius of one. Then this formula was used to
calculate the area of a ten, twenty, forty, eighty, etc. sided
figures.
Formula
Through the application of the Law of Sines and
Pythagorean Theorem, the Formula
was created.
Formula Part Two
Through a series of
mathematical
equations, to calculate
the length of t the
formula
was created.
How the Formula Changes
 Through the application of the previous two formulas, s2n
=
and
be created.
, a new series of formula could
Procedure Three
 Two 2.54 cm lines were draw 2.54 cm apart on am index card.
 Needles were dropped onto the index card. The number of times
the needle dropped and the number of times it landed on a line
were recorded.
 Results were then plugged into Buffon’s formula (2(total
drops)/(number of hits)). Results were recorded.
 Previous two steps were repeated until the formula calculated pi.
 This procedure was tested three times
Detail Analysis
 First procedure: calculated pi to the eighth decimal
place.
 Second procedure: reached the sixth decimal place of pi.
 Third procedure: calculated pi to the third decimal point
after on average 345 needle drops.
Conclusion
 Best Procedure: Using a calculator program was able to
calculate pi furthest decimal place
 Runner-up: Using the formula s2n =
 Least Effective Procedure: Buffon’s Needle Experiment
Further Experimentation and Changes
 Further Experimentation
 The idea of the Golden
Ratio, used in Procedure
Two, can be expanded upon
 Additional methods could be
researched and used to
calculate pi
 Try to reach further decimal
points
 Changes
– Extended time period
– A calculator with a larger
decimal point range for
Procedures One and Two
Reference
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Groleau, R. (2003, September). Approximating pi. Retrieved September 31, 2010, from Nova:
Infinite Secrets database.
Linn, S. L., & Neal, D. K. (2006, March). Approximating pi with the Golden Ratio. The Mathematics
Teacher, 99(7), 472. Retrieved from
http://www.nctm.org//_summary.asp?from=B&uri=MT2006-03-472a
Ralf, I., Doctor Keith, & Doctor Ken. (1996, July 1). Pi in real life [Online forum message].
Retrieved from The Math Forum: Ask Dr. Math: http://mathforum.org//drmath//.html
Reese, G. (n.d.). Buffon’s needle: An analysis and simulation. Retrieved September 31, 2010, from
http://mste.illinois.edu///.html
Slowbe, J. (2007, March). Activities for students: Pi filling, Archimedes style. The Mathematics
Teacher, 100(7), 485. Retrieved from
http://www.nctm.org//article_summary.asp?from=B&uri=MT2007-03-485a
Smith, S. M. (1996). Ancient references to pi; Nine chapters on mathematical art; Brief pi tables;
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history of math (pp. 3-4, 43, 163, 167). Berkley, CA: Key Cirriculum Press. (Original work
published 1996)
Warkentin, D. R. (2009, August). Delving deeper: Janet’s pi-filling hypotheses (Archimedes’
method revisited). The Mathematics Teacher, 103(1), 81. Retrieved from
http://www.nctm.org//article_summary.asp?from=B&uri=MT2009-08-81a