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Say Hi to Pi

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

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Say Hi to Pi

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  1. Say Hi to Pi Katherine Carroll

  2. 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.

  3. Applications of Pi • Class room uses • Physics and aerospace technology • Global Paths and Positioning • Probability

  4. The Life of Pi • Evolution of pi from the Egyptians to Archimedes to SrinivasaRamanujans • Various methods to calculate pi: • Calculator Programs • Creating a Formula • Buffon’s Needle Experiment

  5. Procedure One • Three programs were added to calculator. • Then, the number n was found that estimated pi accurately to the eighth decimal place.

  6. Programs Program TwoProgram Three jjjj 10

  7. 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.

  8. Formula Through the application of the Law of Sines and Pythagorean Theorem, the Formula was created.

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

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

  11. 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

  12. 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.

  13. 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

  14. 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

  15. Reference • 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; Ramanujan’s 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: 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

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