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Exploring Pi: History, Formulas, and Approximations in Mathematics

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Presentation Transcript

  1. Source of pi Approximating Pi through the Ages

  2. Objectives • Students will be able to • different methods of solving for pi and different formulas that use pi. • solve problems using pi-related formulas. • discuss the history and background of pi and its story’s relevance on mathematics curricula today. • use value-based arguments to defend a claim.

  3. Pi Video • http://www.youtube.com/watch?v=SDZ8AzmMOCA • Zero, N. (Producer). (2007). The world without pi . [Web]. • Is Pi really that important to life? • What is Pi?

  4. Within your Groups… • Why was Pi important to the Ancient World? • What are some of the uses of pi? • What formulas use pi? • How was Pi important to the development of modern Mathematics? • Why is it necessary to have a close approximation of pi? • Who sought close approximations of pi? • Come up with at least one problem that uses Pi that an Ancient person would need to solve.

  5. Pi Approximation Race • Each group will get a sheet with different methods for solving Pi. • After 5 minutes of calculation, the group with the closest approximation of Pi is the winner (and gets the prize)! • For this race you can use your calculators for BASIC OPERATIONS ONLY. This means only addition, subtraction, multiplication, and division. • You have to decide which method to use. Which one will get you the closest, quickest?

  6. Post Race • What was the ‘best’ method to use by hand? • What culture developed the Rhind Papyrus? • What other contributions to mathematics were made by non-European mathematicians? • Were the Dark Ages ‘dark’ for the entire world? • http://www.nature.com/news/specials/islamandscience/timeline/index.html

  7. Does math require a historical context? • Why or why not? • Did you know that pi was found in different ways by mathematicians all over the world? • If math is taught without a cultural or historical context, do you assume that it has a multicultural background? • Are teachers obligated to contextualize their math and why ?  

  8. Making Value-Based Arguments • Why are there so many different answers? What are the different values? • Ex) If teachers don’t teach math history, students won’t learn math history, and the whole point of teaching is to transfer knowledge to students! • In this example, the value is the transfer of knowledge, and as long as you think that is most important, the argument is valid. • What is the value for your argument? Which value is most important?

  9. Exit Slips • Hand the completed exit slip to the teacher as you leave class today. You cannot leave until all questions are answered! • You can’t leave until the bell rings either.

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