The number pi has played a big role throughout history in
mathematics. I have also found that it plays a major role on the
internet, so I wrote an internet pi tour to help mathematics students
and others find the best material about it for whatever their interests
are.
Tour
- Ask
Dr. Math
- http://forum.swarthmore.edu/dr.math/faq/faq.pi.html
- This is the best place to start to find out about this much
talked about number. Dr. Math is a feature of the Math Forum, an online
math education community center. This is a good place to clear up many
of the common student confusions about pi and irrational numbers in
general. Most of the commonly asked questions are answered here in the
Pi FAQ and if you don't see your question you can submit it and one of
their knowledgeable volunteers will answer it for you. There are also a
number of good links here for further exploration. Pilinks is a
particularly good one.
- Friends
of Pi Club
- http://www.ast.univie.ac.at/~wasi/PI/
- This is a slightly lighter look at pi. If you really get
interested in pi you can join this club. but you have to meet the
entrance requirement, which is to have the first 100 digits of pi
memorized. But you don't have to be a member to use the page. On this
page you can find out about probably the first recitation of digits of
pi in free-fall, but it is possible to explore more serious interests
as well. You can explore some of the nice pi dedicated pages that some
of the members have created or find out about more sources for pi on
the internet by visiting The Uselessness of pi and its irrational
friends.
- Pi
Mathematics
- http://www.ncsa.uiuc.edu/Edu/RSE/RSEorange/buttons.html
- Next on the tour is an example of the internet being used to
study pi in classes. The Pi Mathematics Project is a
collaborative interdisciplinary project for fifth through eighth
graders.
- Pi
through the ages
-
http://www-groups.dcs.st-and.ac.uk:80/~history/HistTopics/Pi_through_the_ages.html
- The is the best site I have found to start an exploration about
the history of pi. It is part of the MacTutor pages on the history of
mathematics. If you click on 'Rhind Papyrus' you can see a picture of
this ancient Egyptian document. One very nice feature of the Mac Tutor
pages is that they have a large collection of biographies of
mathematicians and the names of the mathematicians mentioned in the
articles are linked to the biographies. Especially to be recommended is
the Archimedes biography with its many links to other material on the
web.
- Pythagorean
Triples
- http://www.access.ch/circle/text1.html
- This is perhaps the most fascinating pi page that I found. It
shows a method similar to that of archimedes for finding approximations
of pi that can be explained without too much trouble to not very
advanced math students. It shows a method for getting as close an
approximation for pi as you like without using anything more
complicated than the Pythagorean Theorem.
- Archimedes'
Approximation of Pi
-
http://itech.fgcu.edu/faculty/clindsey/mhf4404/archimedes/archimedes.html
- Here is another presentation of Archimedes' work on pi. This one
appears to be somewhat closer to Archimedes' original than the one in
MacTutor. It is an annotated version of a translation of the original,
so it is done without the use of trigonometry.
- The
Irrationality of Pi
- http://www.mcs.csuhayward.edu/~malek/Mathlinks/Pi.html
- How do we know that pi is irrational? It was proven by Lambert
in 1761. Here is a proof, but be warned, it takes more than elementary
geometry to understand it.
- The Pi Pages
- http://www.cecm.sfu.ca/pi/
- This page deals mainly with the computation of pi. How are
computers used to find large numbers of digits of pi? This is the place
to find out. Find out about a formula discovered by David Bailey of
NASA/Ames and Peter Borwein and Simon Plouffe of the Centre for
Experimental and Computational Mathematics at Simon Fraser University
for computing the nth digit of pi without the preceding ones. You can
also hear the digits of pi spoken in your choice of a large number of
languages.
- Buffon's
Needle
- http://www.mste.uiuc.edu/reese/buffon/buffon.html
- The next two stops are pages about experimental methods for
finding pi and connections between pi and probability. This one
involves calculating pi by tossing a needle.
- Relative
Primes
- http://www.pvv.unit.no/~eddie/pi/
- In this stop you can participate in a method for computing pi
that has to do with the probability of two numbers randomly chosen
being relative prime.
- Stonehenge
- http://witcombe.sbc.edu/EMIntro.html
- Is there a reason that a group of the stones in Stonehenge loks
like the pi symbol? Some people think there is some mystical connection
between this and the fact that the stones are arranged in a circle.
From this site there are links both to a page about pi and to one about
Stonehenge, so you can make up your mind yourself about the matter.
Keep in mind, though, that the first use of this symbol for pi was in
1706 by William Jones. Ah, but his was Welsh, perhaps that has
something to do with it.
- Pi The Movie
- http://www.pithemovie.com/
- Now for some entertainment, at this stop we go to the movies.
- Contact,
the book
-
http://www.amazon.com/exec/obidos/ASIN/0671004107/o/qid=921074549/sr=2-1/002-5191260-5336253
- Pi also plays a significant role in Carl Sagan's book Contact,
so if you're interested in pi, I highly recommend this book. The movie
is good too, but it leaves out the part about pi, so for that you will
have to read the book.
- The Joy of Pi
- http://www.joyofpi.com/
- At this stop you can learn about another book, one entirely
about pi. There is also a lot you can find out about pi just from these
pages, and there is an excellent page of links. Some links I especially
recommend checking out are the Extraordinary Pi Page, Elias' Pi Page,
and Mike Keith's Poe E: Near a Raven.
- Dale's
Pi Page
- http://www.geocities.com/SiliconValley/Pines/5945/
- At this stop you get to see a page about pi written by 14 year
old Dale Winham in Sioux Falls, South Dakota. It is one of the
nicest pi pages I have seen and has a great variety of fun material.
His 'Fun and interesting facts about Pi' page is particularly to be
recommended and his history page is also quite good.
- The
Pi Trivia Game
- http://www.cid.com/~eveander/trivia/
And now it's time for a quiz.
Additional Links
General
- The
Ridiculously Enhanced Pi Page
- This is the San Francisco Exploratorium's pi page. The main
feature here is the celebration of Pi Day, Mar. 14 at 1:59:26. This is
also Einstein's birthday, which is celebrated with it.
- Daras
Pi Page
- This is a very beautiful page, but it loads slowly.
- Extraordinary
Pi
- This page has a lot of fun facts about pi and also what claims
to be the largest collections of pi links, but it isn't.
- Elias'
Pi Page
- The really interesting thing about this page is that he has
converted the binary expansion of pi both to digitized sound and to a
digitized picture, so you get to hear and see pi. He has then done some
filtering effects on the pictures.
- A
Slice of Pi Home Page
- Paul's
Page of Pi
- A well designed informative site.
- verbose.net
- This is an interesting page, but it is very slow loading.
Mathematics and Computing
- LucyTuning
- LucyScaleDevelopments - Notes on Pi and Phi
- This page has information both on pi and on phi, the ratio of
the sides of the golden rectangle.
- Is
Pi normal?
- Inverse
Symbolic Calculator
- One
Billion Digits of Pi
- Fun
with PI
- This contains the main formulas for computing pi.
- Stu's
Personal pi page
- Timings for PC programs for computing pi. Also some links to
sites having to do with computation of pi.
- Archimedes'
Constant
- This has another presentation of Archimedes Method along with a
number of other things and lots of links and references.
- The
Miraculous Bailey-Borwein-Plouffe Pi Algorithm
- How
to compute digits of pi ?
- This is from the Frequently Asked Questions in Mathematics pages.
- Pi
and the Fibonacci Numbers
- There is a good presentation of the arctan methods for computing
pi here.
Programs
- Armpi
3 - program to calculate pi for the ARM
- apfloat
- Apfloat is a high performance arbitrary precision package. That
means you can do calculations involving millions of digits with it. It
sounds like a good program to download if you want to play around with
computing pi, but I haven't checked it out.
- Computing
Pi
History
- History
of Mathematics - Pi: It Will Blow Your Mind
- A survey on the history of pi with an emphasis on computation
formulas.
- Pi
History
- This is Dale's History of Pi page. It is quite good.
- Yet
another story of pi
- A short survey of the history of pi by Lazarus Mudehwe.
- Pi
in the sky
- Some of the records in the calculation of pi over the centuries.
- Table
of computation of Pi
- This a timeline for when various numbers of digits of pi were
computed.
- PI
in the Bible
- #Y26. PI in the Bible
- Archimedes
and the Computation of Pi
- This has some background information about Archimedes and a
simulation of Archimedes method for finding pi. There are also some pi
and general history of mathematics links.
- Archimedes
and the Square Root of 3
- This is a very interesting page about a conjecture about how
Archimedes estimated the square root of 3, an estimation that was
necessary for his estimation of pi.
- Pi
- Aryabhata's calculation of pi is given in stanza 10 of his
Aryabhatiya. (India 5th c.)
- Indiana
bill sets the value of pi to 3
- The text of the 1897 Indiana State Legislature bill to set the
value of pi to 3.
Biography
- Archimedes
page
- Aryabhata
- Al'Khwarizmi
- MOHAMMAD
BIN MUSA AL-KHAWARIZMI
- Van_Ceulen
- Van
Ceulen's Home Page
- Wallis
- Wallis
John
- Gregory
- Gregory
[Gregorie], James
- Lambert
- Lindemann
- Jones
- Jones,
William
- Ramanujan
Class Projects
- The
Pi Page
- This is a page for a school project about pi. There are some fun
things in it including a joke about cooking a pi complete with a recipe.
- NTTI: How High is Pi?
- WNET National Teacher's Training Institute site. Suggested
activities to accompany a video about pi. Grades 9-12
- Pusic's
Pi Links
- This is a site for a project about finding out about pi through
the internet that was done in a class at Simon Frasier University in
British Columbia.
- Math
Forum: Pi Necklace
- This is a about a suggestion for a Pi Day project from 7th grade
teacher Diana Funke. The idea is to make a necklace with the colors of
the beads representing the different digits.
Art and Entertainment
- A
Pi Poem by Eve
- A poem about pi by Eve Anderson, the writer of the trivia quiz.
- RedFrog
- Poems from the planet Earth - Wislawa Szymborska
- Another poem about pi.
- Poe,
E.: Near a Raven
- Constrained poetry. Mike Keith has constructed a revised version
of Poe's The Raven so that the numbers of letters in successive words
spell out the digits of pi.
- Circle
Digits - A Self-Referential Story
- Another piece of constrained poetry by Mike Keith, this time in
the shape of a circle, but still with the letter counts of the words
spelling out the digits of his favorite number.
- Search
PI
- At this site you can search for a string of digits in pi. Is
your birthday in pi?
- Marko
Nippula's Home Page: Vote on the Future Value of Pi
- Eye
of the Beholder
- This is an interesting story about a possible other universe
where there is a pattern in pi and finding it gives meaning to
somebody's life.
Links
- Pilinks
- This is the best one I have seen for sheer number of links.
- The
Uselessness of Pi and its irrational friends
- Also very good.
- Links
to Pi Pages
- This is the links page from the Joy of Pi homepages. It is very
nicely done with good descriptions of most of the best pages.
- ProsperNet
- Liens
sympa,...
- Pi
- Links categorized as technical or non-technical.
- Yahoo!
Science:Mathematics:Numerical Analysis:Numbers:Specific Numbers:Pi
- Links2Go:
Formulae for Pi
- Links2Go:
Constants
Mathematics
- The Math Forum Home
Page
- Mathematical
Association of America: MAA Online
- Frequently
Asked Questions in Mathematics
- Yahoo!
Science:Mathematics
History of Mathematics
- BSHM:
WWW Resources
- Ancient
Geometry and Insights into the History of Mathematics
- Clark
University History of Mathematics
- Trinity
College Dublin History of Mathematics
- The
MacTutor History of Mathematics Archive
Yahoo!
Science:Mathematics:History