Slide 1

Katherine CarrollSay Hi to PiRationaleDue 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 PiClass room uses

Physics and aerospace technology

Global Paths and Positioning

Probability

The Life of PiEvolution of pi from the Egyptians to Archimedes to Srinivasa Ramanujans

Various methods to calculate pi:Calculator ProgramsCreating a FormulaBuffons Needle ExperimentProcedure OneThree programs were added to calculator.

Then, the number n was found that estimated pi accurately to the eighth decimal place.

ProgramsProgram TwoProgram Three

jjjj 10

Procedure TwoA 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.

FormulaThrough the application of the Law of Sines andPythagorean Theorem, the Formulawas created.

Formula Part Two

Through a series of mathematical equations, to calculate the length of t the formula was created.

How the Formula ChangesThrough the application of the previous two formulas, s2n = and , a new series of formula could be created.

Procedure ThreeTwo 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 Buffons 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 timesDetail AnalysisFirst 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.

ConclusionBest Procedure: Using a calculator program was able to calculate pi furthest decimal place

Runner-up: Using the formula s2n =

Least Effective Procedure: Buffons Needle Experiment

Further Experimentation and ChangesFurther ExperimentationThe idea of the Golden Ratio, used in Procedure Two, can be expanded uponAdditional methods could be researched and used to calculate piTry to reach further decimal pointsChanges

Extended time period

A calculator with a larger decimal point range for Procedures One and TwoReferenceGroleau, 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=MT2006-03-472aRalf, 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//.htmlReese, G. (n.d.). Buffons needle: An analysis and simulation. Retrieved September 31, 2010, from http://mste.illinois.edu///.htmlSlowbe, 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=MT2007-03-485aSmith, S. M. (1996). Ancient references to pi; Nine chapters on mathematical art; Brief pi tables; Ramanujans formulas. In G. Lleuad & C. Mills (Eds.), Agnesi to zeno: Over 100 vignettes from the 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: Janets 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