Pi Patrick Ahern. This is what the symbol for pi looks like.
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Transcript of Pi Patrick Ahern. This is what the symbol for pi looks like.
This is what the symbol for pi looks like.
Introduction
• Rounded to 3.14• Has a national holiday on March 14th
• One of the most recognized symbols to mathematicians
• Irrational• Transendental-is not a root for any number.
Uses
• Used to find the area of circles• Volume of cylinders• Surface area of cylinders• Circumference of circles• Area of only part of a circle
History
• Values of pi in different cultures-Babylonians - 3 1/8, Egyptians - (16/9)^2, Chinese - 3, Hebrews-3
• Archimedes approximated his value of π to about 22/7, which is still a common value today.
• Egyptians and Greeks used it first.
Random Facts
• 16th letter of the Greek alphabet• The symbol for pi (π) has been used regularly
in its mathematical sense only for the past 250 years.
• We can never truly measure the circumference or the area of a circle because we can never truly know the value of pi.
• Albert Einstein was born on Pi Day.
Important Contributors• Archimedes- approximated pi to 22/7• David H. Bailey 29 million and 10 billion'th hexadecimal with all methods. • Fabrice Bellard 50 and 100 billion'th hexadecimal with BBP algorithm. • Jonathan M. Borwein A.G.M. with quartic algorithm. • Peter B. Borwein 10 billion'th hexadecimal with BBP algorithm. A.G.M. with quartic
algorithm. • G.V. Chudnovsky and D.V. Chudnovsky 1, 2 and 4 billion with Chudnovsky formula. By March
1996, more than 8 billion digits have been calculated. • William Gosper 17.5 million digits with Ramanujan formula. • Guilloud and Bouyer 250,000, 500,000, 1 million and 2 million with arctan formulas.. • Daniel Shanks and John Wrench Jr. 100,265 in 1961 with arctan formulas. • Yasumasa Kanada 2 million and 10 million decimal with arctan method, 100 million
hexadecimal digits with A.G.M. and the other records from 4 million decimal in 1982 up to 6,442,000,000 decimal in 1995 with A.G.M. methods.
• Simon Plouffe 10 billion'th hexadecimal with BBP algorithm. • Daisuke Takahashi 100 million hexadecimal digits with A.G.M. and 3.2 billion, 4.2 billion and
6.4 billion decimal with A.G.M. methods.
Q and A
Q-Does Pi ever end?A- No, Pi is a never ending, non-repeating decimal.Q-How old is Pi?A- Pi is the 16th letter in the greek alphabet. The
oldest recorded history is from 1900-1680 BCE, on a Babylonian tablet.
Q- What is the world record for most digits of pi recited?
A-Chao Lu of China recited 67,890 decimal places on 20 November 2005.
Contributing Cultures/countries
• China-most digits recited• Japan-most digits discovered by
supercomputer• Egyptians-Great Pyramid at Giza has a ratio of
1760/280, perimeter to height. That ratio is equal to 2(pi)
• Flemish mathematician Adriaan van Roomen arrived at 15 decimal places in 1593.
Bibliography- Special Thanks to:
• http://mathworld.wolfram.com/Pi.html• http://www.math.com/tables/constants/pi.htm• http://library.thinkquest.org/C0110195/uses/us
es.html• http://facts.randomhistory.com/2009/07/03_pi
.html• http://www.pi-world-ranking-list.com/news/in
dex.html• http://oldweb.cecm.sfu.ca/projects/ISC/people
.html• http://ualr.edu/lasmoller/pi.html• http://en.wikipedia.org/wiki/Pi
