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Constructing Pi

Constructing Pi. Stefanie Martino. Objective: The learner will demonstrate the origin of pi by measuring the circumference and diameter of different objects. The learner will create the equation to find the circumference of a circle, given its diameter or radius.

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Constructing Pi

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  1. Constructing Pi Stefanie Martino

  2. Objective:The learner will demonstrate the origin of pi by measuring the circumference and diameter of different objects.The learner will create the equation to find the circumference of a circle, given its diameter or radius.

  3. http://www.youtube.com/watch?v=ldnZevLaX6I&feature=related

  4. Elements Relating to Pi • Circumference • Diameter • Radius

  5. History of Pi • Some historians break the development of pi into three periods • Geometrical Period • Classical Period • Computer Age

  6. Geometrical Period • Ancient Egyptian, Babylonian, Indian, and Greek geometers knew pi was slightly more than 3. • Babylonia: 25/8 • Egypt: 256/81 • India:339/108 • Hebrew Bible: 3

  7. Geometrical Period • Archimedes- first to rigorously estimate pi. • Found that by calculating the perimeters of polygons that a circle is inscribed in, pi can be estimated. • 96-gon… concluded that 223/71 < π < 22/7 • *handout

  8. Classical Period • The next major advance in determining pi came with the development of infinite series and calculus. • Around 1400, MadhavaofSangamagrama found the first known series: • Takes too long to get to pi (Guess how many terms are needed to come close to Archimedes estimation!) http://en.wikipedia.org/wiki/Pi

  9. Classical Period • German mathematician Ludolph van Ceulen (1540-1610) • Produced geometric method that determined 35 decimal places! • So proud of his work, he engraved these digits onto his tombstone • 1706: John Machin was the first to compute the first 100 digits of pi.

  10. Computer Age • In the 20th century, the launch of computers led to an improvement of pi calculations. • ENIAC (Electronic Numerical Integrator and Computer) was first used in calculations for the hydrogen bomb! • 1949: John von Neumann used it to compute 2037 digits of pi.

  11. Computer Age • 1973: hit the million digit mark due to faster hardware and new algorithms • 1987- Chudnovsky brothers came up with a new series: • Used in the first calculation of over 1 billion digits. • Remains the formula for pi calculations in personal computers

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