# Pi Day Resources

## General Pi

2.    A Common Book of Pi    http://personal.bgsu.edu/~carother/pi/Pi1.html

3.    Slashdot Pi Day   http://slashdot.org/articles/01/03/14/1622217.shtml

4.    Pi World    http://www.piworld.de/

5.   Joy of Pi    http://www.joyofpi.com/

6.    Pi Links    http://www.joyofpi.com/pilinks.htm

7.    My Pi Day Web Site    http://homework.syosset.k12.ny.us/teachers/bwaldner/

9.    Pi (1998) http://www.reel.com/movie.asp?MID=41906

10.   Pi in the Sky    http://www.pims.math.ca/pi/index.html

11.   Friends of Pi    http://www.astro.univie.ac.at/~wasi/PI/

12.   The World of Pi (Interesting Pi Facts)    http://www.wpdpi.com/index.shtml

13.   Pi Unleashed    http://www.jjj.de/pibook/pibook.html

14.  Jim Loy's excellent website for a variety math topics   http:/www.jimloy.com/geometry/piz.htm

## Sierpinski and Einstein (Both Have Birthdays on Pi Day)

1.    Sierpinski Gasket    http://www.cut-the-knot.com/triangle/Hanoi.html

2.    Einstein   http://www.aip.org/history/einstein/

3.    Chaos Game – a few simple rules generate Siepinski's Triangle   http://math.bu.edu/DYSYS/chaos-game/chaos-game.html

4.    The Magic Sierpinski Triangle   http://serendip.brynmawr.edu/complexity/sierpinski.html

5.    The Sierpinski Problem   http://www.prothsearch.net/sier.html

6.    The Sierpinski Champs at Pacoima Middle School   See their amazing, 35 feet by 35 feet, Sierpinski Triangle prepared by Vladimir Litt's 7th graders.  http://math.rice.edu/~lanius/frac/pacoima.html

## Historical Pi

1.    Willam Jones - first use of  Pi as math symbol (1706)  http://es.rice.edu/ES/humsoc/Galileo/Catalog/Files/jones.html

2.    Carl Lindemann  http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Lindemann.html

3.    The MacTutor History of  Mathematics (Scotland) http://www-history.mcs.st-andrews.ac.uk/history/index.html

## School Activities

1.    Annual Pi Day Contest (NCMTA)   http://www.mathmuseum.org/

2.    Pi Day Activities (Excellent Elementary through High School Activities)   http://www.mathwithmrherte.com/pi_day.htm

3.    Middle School Pi Day    http://www.germantownacademy.org/academics/MS/PiDay/Index.htm

4.    Pi Beads (Elementary or Middle School)    http://www.contrib.andrew.cmu.edu/~shuma/pibeads/

5.    Pi Day Assembly    http://www.germantownacademy.org/academics/MS/PiDay/Assembly.htm

6.    Teacher’s Corner National Pi Day    http://www.ael.org/eisen/treasure/tc0300.htm

7.    Teacher2Teacher    http://forum.swarthmore.edu/t2t/faq/faq.pi.html

8.    Misadventures of Sailor Pi (very cute)    http://members.aol.com/LooseTooth/sailorpi.html

9.    Pi Trivia Game (quizzes on Pi history)    http://eveander.com/trivia/

10.   Pi Programs TI-83    http://www.mathwithmrherte.com/pi_programs.htm

11.   Archimedes’ Method for Pi  http://personal.bgsu.edu/~carother/pi/Pi3a.html

12.   Buffon’s Needles Lab  http://www.efg2.com/Lab/Mathematics/Buffon.htm

13.   Buffon’s Needle Problem   http://www.mste.uiuc.edu/reese/buffon/buffon.html

14.   Compte de Buffon  http://www.cut-the-knot.com/ctk/August2001.html

15.   Buffon’s Needle Problem  http://www.cut-the-knot.com/fta/Buffon/buffon9.html

16.   The Theorem of Barbier  http://www.cut-the-knot.com/ctk/Barbier.html

17.   Pi and the Fibonacci Numbers   http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibpi.html

18.   The Pi Function, pi(x) (The Prime Number Theorem)  http://www.utm.edu/research/primes/howmany.shtml#hist

## Advanced Pi

1.    Pi-Calculus Links     http://www.cwi.nl/~arie/picalc.html

2.    Calculating Pi using Calculus    http://www.ams.org/new-in-math/cover/pi-calc.html

3.    Pi Talks (Advanced)   http://www.cecm.sfu.ca/personal/jborwein/Pi_Talk.html

4.    Princeton Pi Ref Paper    http://es.rice.edu/ES/humsoc/Galileo/Catalog/Files/jones.html

5.    The Pi Pages (Advanced)   http://www.cecm.sfu.ca/~pborwein/

6.    Pi: A 2000-Year Search Changes Direction (Mathematica used for Digit Extraction)  http://www-2.cs.cmu.edu/~adamchik/articles/pi/pi.htm

7.    A C++ Pi Program for Extracting Hex Digits   http://pw1.netcom.com/~hjsmith/Pi/PiQPCpp.html

## Happy Pi Day Cards

1.    Send a Bluemountain Happy Pi Day Card (free)    http://free.bluemountain.com/engx/daleb/UNH_pi.html or http://free2.bluemountain.com/cards/boxb228752h5/kitwbgnvnm3wmys.html

2.    Pi Day Greeting Cards (select ‘Events Calendar’; several popup ads on this site)   http://www.123greetings.com/events/pi_day/

3.    Pi Day Cards, Einstein’s B-Day   http://webmaniadesigns.com/cards/uselessholidays/pi_day.shtml

## Pi Day Attire

1.    Pi T-shirts, Ties and Scarves  (The Science Teecher  1-877-286-6212)   ‘Pi in Sky’, ‘Have Your Pi and e It Too’ and others   http://www.scienceteecher.com/math_shirt.html or for club discounts http://www.scienceteecher.com/clubdiscount.html

2.    Pi T-shirts    http://www.gaftee.com/index.html

3.    ‘Cow Pi’ T-shirts (What on Earth  1-800-945-2552)    http://www.whatonearthcatalog.com/cgi-bin/hazel.cgi?randomizer=123569951&client=76932016&action=serve&item=temp_new.html&ID=3AP&SECTION=2

4.    Pi Cologne from Givenchy   http://www.perfumemart.com/htmlii/Pi_Men_11522-33.html

## Fine Arts Pi

1.    The Pi Symphony by Lars Erickson.   An orchestral work whose melodic content is derived from the transcendental number Pi. You can purchase a CD of the synthesized version for \$15.00. http://www.pisymphony.com/index.html

2.    Happy Pi Day Songs    http://www.winternet.com/~mchristi/piday.html

3.    Bill Crozier at Entrophy  (MP3.com).  A moody song based on the digits of pi.

http://artists.mp3s.com/artist_song/1024/1024679.html

http://users.snip.net/~wcrozier/entropy/songs.html

4.    Pi the Movie (clips, sound track, related genre)   http://www.pithemovie.com/pithemovie.html

5.    Math in the Movie  http://world.std.com/~reinhold/mathmovies.html

7.    American Pi (the day the math team tied)    http://www.geocities.com/CollegePark/Plaza/9252/pisongs.html

8.    Earth Mysteries (The Mountains of Pi)  http://witcombe.sbc.edu/earthmysteries/EMPi.html

9.    Sliding Pi   (mosaic tile hues in Toronto subway station based on pi)  http://www.maa.org/mathland/mathtrek_6_5_00.html

10.    'A Song about Pi' and 'That's Mathematics'  (to the tone of That's Entertainment) by Irving Kaplansky  http://www.maa.org/mathland/mathtrek_7_12_99.html

## Pi Humor

1.    Pi Jokes    http://www.wpdpi.com/jokes.shtml

2.    Math Comics    http://www.csun.edu/~hcmth014/Comics.html

## Pi Day Fund Raiser

1.    The Order of Pi (fraternity fund raiser)   http://www.engr.uvic.ca/~pi/

## Digits of Pi and Searches

1.    The Pi Searcher (searches the first 100 million digits of pi for any string of digits) http://wwwangio.net/pi/piquery

2.    Digits of Pi (select landscape printing)   http://students.washington.edu/~chahm/pi/5000.html

3.    Pi to Million Digits    http://www.cecm.sfu.ca/organics/papers/borwein/paper/html/local/billdigits.html

4.    Pi Club (How many digits of Pi do you know?) http://www.albanyconsort.com/pi

5.    Find Your Birth Date in Pi     http://www.facade.com/legacy/amiinpi/

6.     Pi Shared Fairly (Normality of Pi)   http://www.nature.com/msu/010802/010802-9.html

7.    The Search for Intelligence in Pi   http://members.aol.com/spoons1000/pi/index.html

8.    The Incredible Pi Code (Ivars Peterson's MathTrek)  http://www.maa.org/mathland/mathtrek_4_1_00.html

9.    A Passion for Pi (mnemonic devices to remembering the digits of pi) http://www.maa.org/mathland/mathland_3_11.html

## Pi Books and Videos

1.     Pi Videos – ‘The Story of Pi’ and ‘The Early History of Mathematics’ (\$34.90 with workbook) For a detailed description, go to www.projectmathematics.com. Order from http://www.bookstore.caltech.edu/ ( select video & mixed media)or call 1-800-514-2665.

2.    Pi Books (History of Pi, The Joy of Pi, Pi: A Source Book, Sir Cumference and the Dragon of Pi, Sir Cumference and the First Round Table )   http://www.wpdpi.com/store.shtml

3.    Pi: A Source Book by Lenhart Berggren, Jonathan Borwein and Peter Borwein, 2nd ed., 1997, Springer, 736 pp., ISBN 0-387-98946-3.  This book is a collection of articles following pi from the early days of mathematics to the present.  This is a book for every high school library (IMC).   http://www.amazon.com

4.    Elementary and middle schoolers will enjoy Sir Cumference and the First Round Table by Cindy Neuschwander, Charlesbridge Publications.  Also Sir Cumference and the Dragon of Pi.    http://www.amazon.com

5.    Journey Through Genius by William Dunham, and A History of the Circle by Ernest Zebrowski are appropriate for high school.   http://www.amazon.com

6.    Classroom Ready Pi Activities for Grades 6-8, A Piece of Pi by Naila Bokhari, pp. 48, \$9.95, ISBN 1-883055-43-1, Dandy Lion Publications, 1-805-543-3332

## Pi in The Bible

1.    Pi in the Bible    http://www.yfiles.com/pi.html

## International Connections of Pi

1.    L’univers de Pi (in French)   http://www.multimania.com/bgourevitch/

2.    Zirkumferenz  (in German)   http://www.zirkumferenz.de/

3.    Pi (in Spanish)   http://webs.adam.es/rllorens/pihome.htm

4.    Le Nombre Pi (in French)   http://trucsmaths.free.fr/Pi.htm

5.    Magic Pi World (in German and English)  http://www.jvshly.de/piworld/mpw_home.htm

P

# The First Use of 

Gene Potter

Did you ever have a student ask, “Where did  come from?”  I often answered with a little history back to the Babylonians.  But another spin to the question might be that of who first used the symbol  for the all-familiar value of pi.

Asking math students to do a little historical research can easily result in more than a few moans.  You can motivate their interest by examining The Pi Trivia Game by Eve Anderson at http://eveander.com/trivia/ to create a competitive classroom challenge, and knowing your pi history is a helpful edge in this trivia game. High school students find that this Web site challenges their knowledge of pi.  You will certainly want to add this Web site to your activities on March 14, Pi Day.

## William Jones

The sixteenth letter of the Greek alphabet, , was first used for the familiar value 3.1415… in the publication, “Synopsis Palmariorium Mathesios”, authored by William Jones in 1706. “Synopsis Palmariorium Mathesios” was a text that included some lessons related to Newton’s fluxions among several other mathematical topics.  Jones associated the word ‘periphery’ with the value pi and in parentheses shows the Greek letter .  He provides no explanation for the selection or use. It is believed by many that the Greek word ‘perimetron, ’ derived from ‘peri’ (around) and ‘metrein’ (to measure) is the desired reference with  being the first letter of the Greek spelling. However, the popularization of the symbol  is often credited to the prolific writings of Leonard Euler (1707-1783).

William Jones was born on a small farm in Wales in 1675.  Little is known of his formal education.  However, it is known that he taught mathematics on a British ship in the Indies, and later tutored the future President of the Royal Society, Thomas Parker.

Jones also published “Newton’s De Analysis” (an analysis of Newton’s work), “A New Compendium of the Whole Art of Navigation”, and “Introduction to the Mathematics.”  He was a friend of Newton, and it is believed that he reviewed and edited some of Newton’s manuscripts.  After being elected Vice-president of the Royal Society, he was instrumental in settling the dispute between Sir Isaac Newton and Baron Gottfried von Leibnitz regarding the propriety claims to the authorship of calculus.

Today, many schools around the globe celebrate Pi Day. It's a wonderful opportunity for us to see our students in a rich light as we move beyond the formality of curriculum with our joy of mathematics. Let's not forget that 2006 will be the 300th Anniversary of the introduction of the symbol . I invite you to celebrate Pi Day in as many creative pedagogical venues as possible.

References

Van Helden, Albert. “Jones, William.” http://es.rice.edu/ES/humsoc/Galileo/Catalog/Files/jones.html.  2001.

Berggren, Lennart, Jonathan Borwein, and Peter Borwein. Pi: A Source Book. New York: Springer, 2000.

(Printed in the Missouri Council of Teachers of Mathematics Bulletin, the Mathematics Educators of Greater St. Louis Newsletter, January 2002, and the Ontario Association for Mathematics Education Ontario Mathematics Gazette, December, 2004)     ■

# Digits of Pi

(groups of 10; 100 per line)

Pi 3.

1415926535 8979323846  2643383279 5028841971  6939937510 5820974944  5923078164 0628620899  8628034825 3421170679 8214808651 3282306647  0938446095 5058223172  5359408128 4811174502  8410270193 8521105559  6446229489 5493038196 4428810975 6659334461  2847564823 3786783165  2712019091 4564856692  3460348610 4543266482  1339360726 0249141273 7245870066 0631558817  4881520920 9628292540  9171536436 7892590360  0113305305 4882046652  1384146951 9415116094 3305727036 5759591953  0921861173 8193261179  3105118548 0744623799  6274956735 1885752724  8912279381 8301194912

(500 Digits)

9833673362 4406566430  8602139494 6395224737  1907021798 6094370277  0539217176 2931767523  8467481846 7669405132 0005681271 4526356082  7785771342 7577896091  7363717872 1468440901  2249534301 4654958537  1050792279 6892589235 4201995611 2129021960  8640344181 5981362977  4771309960 5187072113  4999999837 2978049951  0597317328 1609631859 5024459455 3469083026  4252230825 3344685035  2619311881 7101000313  7838752886 5875332083  8142061717 7669147303 5982534904 2875546873  1159562863 8823537875  9375195778 1857780532  1712268066 1300192787  6611195909 2164201989

(1,000 Digits)

# A Contest Reciting the Digits of Pi

Gene Potter

If you decide to conduct a Pi Digits Contest, you might be surprised at the results - as was a friend of mine in San Jose, California.  This is his Pi Digits Contest story.  He offered a huge, very huge, stuffed cloth bear as a prize to any student in his first-year algebra classes who could accurately recite the most digits of pi.

The lull of winter had taken its toll and Pi Day was an excellent chance to re-energize the class.  He announced the contest and offered the prize.  It worked, the class snapped into a frenzy of excitement.  Pi Day came; the contest began. No one in the class, nor in the school, and certainly not the teacher could believe who won – the most difficult student in the school – straight Fs, straight zeros, and absolutely no cooperation.

The presence of this young man walking to the front of the room uncomfortably quelled the class.  He cautiously began reciting the digits of pi.  They were transfixed with each digit; no one dared break his concentration.  After missing on the 221st digit, there was a very brief moment of silence, then the class stood, cheered and applauded.  He knew he had changed.

Imagine the sight of your school's tough guy reciting 220 digits of pi and clutching an over-sized stuffed teddy bear.  What a transformation!

Now, let me share with you how Elaine Harke, Mathematics Department Chair at Hazelwood West High School (Missouri), conducted her Pi Digits Contest.  She announced that the contest would take place during 6th period on Pi Day.  A few weeks before the eventful day, she distributed a sheet with 1,000 digits of pi.

On Pi Day, students went to the Wildcat Cafe, signed in, and were called before a panel of four students to recite.  The panel checked the accuracy of the digits and recorded results.  Each student was given two attempts.

At the end of the period, a trophy, a Pi Day T-shirt, Pi cologne, and McDonald's Apple Pies were awarded to the top students.   The first place trophy went to a student who recited 314 digits.  He stated that he knew more digits, but thought it would be cool to stop at 314.  Everyone had some fun and gained a little more respect for each other.

Incidentally, the world record for reciting digits of pi was set in 1995 by Hiroyuki Goto who recited over 42,000 digits of pi.  What's your school record?

# Pi Day Fund Raiser for St. Jude Children's Research Hospital

Patricia Kennedy, Kirby Middle School, raised over \$100 on Pi Day for St. Jude Children's Research Hospital.  During lunch, several teachers volunteered to be targets for shaving-cream pieings by students.  Students paid 25 cents to pie a teacher.  I'll bet she could have charged substantially more.  Teachers placed their faces through openings in a sheet of protective cardboard, and wore goggles and shower caps.   Another lunchtime venue sported a pie-eating contest with students paying \$3.14 to enter.

Prior to Pi Day, a raffled was held to see who would get to be the first digit, the '3', and who would be the runner-up, the 'decimal point.' The next morning, a human pi chain was formed outside the school with each student holding up a digit of pi and of course, the decimal point.  ■

# Slicing Up Pi Day

Jane Turley, Woodstock High School, reports that she serves pi for Pi Day.  She uses cupcake liners as the pans, vanilla wafers as the crust, assorted pie fillings (cherry and puddings seem to be the favorites), and a little cool whip.

After putting their pies together, she challenges her students with a classic math problem.  What is the largest number of pieces that one can get with exactly six straight cuts of a pie?  The pieces need not be equal.   Students might be asked to make a table of the number of cuts verses the number of pieces.  She encourages her students to make a graph.  Then, they are asked to carefully write a method for getting a solution if they were to make seven cuts. She concludes the lesson with a little algebraic-thinking by asking them to generalize the solution if they were  making n cuts.

The Pi Symphony

The Pi symphony is an orchestral work whose melodic content is derived from the number pi. Lars Erickson has scored the pi symphony by assigning notes to the digits of pi for various instruments. If you want to know more about the Pi Symphony, e-mail Lars Erickson, lars@pisymphony.com.   If you don't happen to have an orchestra handy, Lars will let you buy a CD or a copy of the master score of the melodic rendition of Pi Symphony. ■

P

# Pi-oneers

• Before pi, mathematicians would write:

"the quality which, when the diameter is multiplied by it, yields the circumference"

The Joy of Pi by David Blatner

• In Germany, pi is sometimes referred to as the Ludolfian number in honor of Ludolf van Ceulen who spent his life calculating pi.

• The most famous formula relating the five most frequent constants in mathematics is Euler's Formula,

• Archimedes (c.250 BC) proved that the area of a circle with radius r was equal to the area of this right triangle.

2 π r

r

• In 1655, John Wallis proves:

• In 1579, Francois Viete proves using Archimedes method that

• In 1675, James Gregory  proves

• In 1761, Johann Lambert proves that pi is irrational by first proving that if tan (x) is rational that x must be irrational.  Thus, since tan (π/4)=1 then π must be irrational.

• In 1811, Karl Gauss introduces a capital pi π for product notation.

• Using the Taylor expansion for sin x, Leonard Euler, in 1736, gave us a remarkable proof for:

• He then proves:

• The probability that two randomly selected integers are relatively prime is

• The probability that two randomly selected points on a lattice are directly connected, without any other points between them, is

• Around 1670, Isaac Newton  calculates pi to 16 decimal places based on the binomial expansion of

• John Machin (c.1750) proves

• In 1914, Srinivasa Ramanujan  proves

• In 1996, David Bailey, Peter Borwein and Simon Plouffe prove:

• Bell Curve – Normal Curve  - Gaussian Probability Distribution of a standardized random variable

• 1996, Michael Keith created a poem making the word length a mnemonic for pi.  His poem encodes the first 740 digits of pi, beginning with 'Poe' (3).  A word with 10 letters represents the digit 0.  Words with more than 10 letters (99 or less) represent two digits.

Poe, E. - Near A Raven  (3.1415)

Midnights so dreary, tired and weary.  (926535)

Silently pondering volumes extolling all by-now obsolete lore.

During my rather long nap – the weirdest tap!

An ominous vibrating sound disturbing my chamber's antedoor.

"This", I whispered quietly, "I ignore".

Perfectly, the intellect remembers: the ghostly fires, a glittering ember.

Inflamed by lightning's outburst, windows cast penumbras upon this floor.

Sorrowful, as one mistreated, unhappy thoughts I heeded:

That inimitable lesson in elegance – Lenore –

Is delighting, exciting…nevermore.

Ominously, curtain parted (my serenity outsmarted),

And fear overcame my being – the fear of "forevermore".

Fearful foreboding abided, selfish sentiment confided,

As I said, "Methinks mysterious traveler knocks afore.

A man is visiting, of age threescore."

Taking little time, briskly addressing something: "Sirs," (robustly)

"Tell what source originates clamorous noise afore?

Disturbing sleep unkindly, is it you a-tapping, so slyly?

Why, devil incarnate! --" Here completely unveiled I my antedoor;

Just darkness, I ascertained – nothing more.

The remainder of the poem can be found in Pi: A Source Book, pp. 659-662.