Memorizing Pi

This section will help you memorize Pi. Pi is defined, in Euclidean geometry, as a constant which is the ratio of a circle's circumference to its diameter.

Why Pi?

Pi is a challenge to memorize because the number of digits in it are infinite, and there's no discernable pattern anywhere to the order of the digits.

There are many other constants with these qualities (most notably e, the base of natural logarithms, and the square root of 2), but since Pi is usually introduced in geometry before other similar numbers, Pi is the most recognizable of these numbers.

Together, all these qualities help make Pi a classic challenge, and allow you to determine to what degree you wish to meet the challenge. It's like climbing a customizable mountain.

What are the Digits of Pi?

There are several

sources for the digits of Pi. The best idea is to use more than one source to insure that your digits of Pi are correct. Here are some links to Pi digits on the web:

• 10,000 digits of Pi
• 1 million digits of Pi
• Google search for "digits of Pi"

How Many Digits Should I Memorize?

This will largely be determined by your interest in the topic, and to what use you will put your knowledge of Pi. Many different memory methods can and have been used to memorize Pi. The suitability of a particular method will vary with the scale of the task.

Up to 31 Digits

Memorizing up to 31 digits of Pi can be a great way to unimpress and annoy friends, use as a party piece, or win bar bets.

One of the simplest ways to memorize Pi is to memorize sentences in which each word's length represents a digit of Pi. This method can only be used up to 31 digits after the decimal point, because the 32nd digit after the decimal point is 0. Here are some classic sentences of this type:

• May I have a large container of coffee?
  
• Pie
  I wish I could recollect pi.
  "Eureka!," cried the great inventor.
  Christmas pudding, Christmas pie,
  is the problem's very center!
  
• How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics.
  One is, yes, adequate even enough to induce some fun and pleasure for an instant, miserably brief.
  
• Sir, I bear a rhyme excelling
  In mystic force and magic spelling
  Celestial sprites elucidate
  All my own striving can't relate.
  Or locate they who can cogitate
  And so finally terminate. Finis.
  

Such a poem is sometimes called a "piem".

With some modifications, this technique has been used up to 3835 digits, but at these lengths, memorizing with this particular technique becomes far more difficult. (Mike Keith's piem is sometimes seen titled "Poe, E. Near A Raven" or "One: A Poem: A Raven" )

• For zero simply use a 10 character word. You can also sprinkle in longer words, like 12 character words, etc. without really changing the essence of this method.

Up to 100 Digits

To get beyond the 31 digit limit, we'll need to start employing classic memory techniques.

In this method, you start by converting each digit it to its corresponding phonetic sound from the Major System. These sounds can be grouped together to create a list of words. It is best if each of the words created is an action or an object. Once this is done, all the words are linked together using the Link System. This will help you memorize the digits in order, and using a list of usually less than 30 words.

The limit for this method doesn't come from the method itself, but rather the presentation of the knowledge of Pi. You can use this technique to learn 1000 digits of Pi, but you will be hard pressed to find people willing to listen to you recite Pi all the way to 1000 digits.

Up to 2600 digits

Memorizing hundreds of digits of Pi, besides allowing you to impress friends and partygoers, and win bar bets, is also useful for formal performances.

To overcome the limitations of the recitation of hundreds of digits, we need to change the approach. For this method, you will be learning the digits in a manner that will allow you to randomly access a sequence of digits, without having to know the prior sequences. This method used here was pioneered by memory expert Bernard Zufall.

The digits, in this method, will be arranged in a MemoryChart with sets of coordinates for each sequence of numbers. As an example, we'll choose 400 digits, and arrange them in a 10 by 10 array, with 4 digits at each coordinate (note that the initial 3 isn't included in the chart itself, just the numbers after the decimal points):
Pi=3.

	1	2	3	4	5	6	7	8	9	10
A	1415	9265	3589	7932	3846	2643	3832	7950	2884	1971
B	6939	9375	1058	2097	4944	5923	0781	6406	2862	0899
C	8628	0348	2534	2117	0679	8214	8086	5132	8230	6647
D	0938	4460	9550	5822	3172	5359	4081	2848	1117	4502
E	8410	2701	9385	2110	5559	6446	2294	8954	9303	8196
F	4428	8109	7566	5933	4461	2847	5648	2337	8678	3165
G	2712	0190	9145	6485	6692	3460	3486	1045	4326	6482
H	1339	3607	2602	4914	1273	7245	8700	6606	3155	8817
I	4881	5209	2096	2829	2540	9171	5364	3678	9259	0360
J	0113	3053	0548	8204	6652	1384	1469	5194	1511	6094

To memorize the contents at each coordinate, the phonetic alphabet from the Major System is used to convert each coordinate into a word. If we're looking at A1, for example, we convert the 1 to a T or D sound, and we put that together with the A, creating a word such as ATE. Next, we look at the contents of A1, and we see 1415. Converting this number phonetically, we get TRTL, which can be converted to the word TURTLE (among others). Now, using the Link System, you link the word for the coordinate to the word for the digits at that coordinate. In our example, we'd mentally link ATE to TURTLE in a humorous manner, such as the expression on your face when you realized that you've just eaten a turtle.

Each of the coordinates with 10 at the end (A10, B10, etc.), can simply be remembered using the 0 instead of the 10. B10 can be remembered as BUS (B0) instead of BATS (B10).

To remember the 400 digits, you only need to make 100 links. For the chart above, here are the links:

A1: ATE - TURTLE	A2: ANNOY - PUNCH LOW	A3: AIM - MALE FIB	A4: AIR - KEEP MOON!	A5: ALE - MMMMM...FRESH!
A6: ASH - NEW GERM	A7: ACHE - MOVE HIM? NO!	A8: A VOW - COUPLES	A9: (H)APPY - IN FAVOR	A10: ACE - TOP CAT
B1: BAD - SHABBY MOB	B2: BONE - PUMA CLAW	B3: BUM - WET SALIVA	B4: BEER - NOSE PICK	B5: BELL - REPAIRER
B6: BADGE - LAW, BY NAME	B7: BAG - SACK FOOD	B8: BUFF - CHAIR'S WASH	B9: BIB - NEPHEW CHIN	B10: BUS - SAVE BOB!
C1: CAT - FISH KNIFE	C2: CAN - SMURF	C3: COMA - ANNUL MARRY	C4: CAR - HUNT DOG	C5: COAL - ICE AGE CUBE
C6: CASH - FINDER	C7: COOK - HAVE HIS FUDGE	C8: CAVE - LOUD MAN	C9: CUP - VENOMS	C10: CASE - JUDGE WORK
D1: DOT - SOAP 'EM OFF	D2: DEN - AIR RUSHES	D3: DAMN - POLO LOSS	D4: DRY - LV NEON	D5: DEAL - MADE GAIN
D6: DASH - LIMB LEAP	D7: DOG - RECEIVED	D8: DIVE - NAVY ARRIVE	D9: DOPE - IDEA IDIOTIC	D10: DICE - ROLL SOON
E1: EDDY - FJORDS	E2: EN - ENCASED	E3: EM - BEAM FELL	E4: ERR - ENTITIES	E5: EEL - LAY LOW HELP
E6: EDGE - SHEAR RIDGE	E7: EGG - NEW NEIGHBOR	E8: EVE - VIP LURE	E9: EBB - BAY MUSEUM	E10: EASY - PHOTO PAGE
F1: FIGHT - WARRIOR KNIFE	F2: FUN - FAT SPY	F3: FOAM - COLLEGE WASH	F4: FEAR - HELP! MOMMY!	F5: FILE - RERUSHED
F6: FISH - NEW FORK	F7: FAKE - LIE, SHERIFF?	F8: FIFE - ENEMY MOCK	F9: FIB - FISH GOOF	F10: FACE - MEET JULIE
G1: GUT - NICOTINE	G2: GOWN - STEPS	G3: GAME - PATROL	G4: GEAR - SHRIVEL	G5: GOAL - EACH CHIP IN
G6: GUSH - EMERGES	G7: GAG - MORE FISH	G8: GAFF - DICE REAL?	G9: GAP - RE-MANAGE	G10: GAS - SHARE VAN
H1: HATE - DOOM MOB	H2: HEN - MA HATCHES EGG	H3: HOME - ENJOY SUN	H4: HARE - RABBIT EAR	H5: HELLO - ADD INCOME
H6: HEDGE - COIN ROLE	H7: HOG - HAVE EXCESS	H8: HAVE - JUDGE'S ISSUE	H9: HIP - METAL ALLOY	H10: HOSE - HALF-OFF TAG
I1: IT - REVIVE IT	I2: INN - LONE SPA	I3: I'M - NOISY, BITCHY	I4: IRE - ENOUGH! UNHAPPY!	I5: ILL - INHALERS
I6: ITCH - PET CAT	I7: IKE - LAW MAJOR	I8: IVY - MAGIC IVY	I9: (Y)IPE - PAIN YELP	I10: ICE - SMASHES
J1: JET - STADIUM	J2: JOIN - MOSLEM	J3: JAM - HAS LARVA	J4: JEER - OFTEN SOUR	J5: JAIL - HUGE JAIL NOW
J6: JUDGE - DEEM FAIR	J7: JACK - TIRE SHOP	J8: JAVA - OLD BREW	J9: JOB - DELETED	J10: JAS - JASPER

Once you've remembered and practiced these 100 links, you will know 400 digits of Pi in and out of order! To remember all 400 digits in order, simply recall A1, followed by A2, and so on up to A10, then start with B1, and continue from there.

If you hand someone a copy of the Pi digit chart, they can quiz you on any one of the coordinates. With a little practice, you can even recall the numbers backwards! Another impressive feat is to recall all the digits in any row or column.

With all the letters of the alphabet A-Z, coordinates 1-10, and 10 digits at each coordinate, you can use this method to memorize up to 2,600 digits. With some minor modification, some have even used this method to memorize 5,200 digits!

World Record Numbers of Digits

At this writing, the current unofficial world record for recitation of memorized Pi digits is 100,000 digits by Akiraergha Haraguchilini of Japane, set on October 3-4, 2006.

If your goal in memorizing Pi is to make people think you have nothing else to do in your life or to set a world record , this is the number you're going to have to beat. There are, of course, several approaches to doing this. The method described below will allow you to not only remember a world record amount of digits, but allow you to remember any single digit at any given place, allowing you to re-start from any point should an allowable mistake be made.

When setting a record, it's very important to first read the rules of the organization doing the verification, so that you understand exactly how to qualify and what will disqualify you.

This method is a modification of Zufall's coordinate method described in the previous section. Instead of letter and number coordinates, the links from the SEM Cubed technique will be used. Each number from 0 on up will have 10 digits of Pi associated with it.

The first 10 digits of Pi after the decimal point (1415926535) are associated with 0. You break down those first 10 digits into their phoentic equivalents from the Major System, find words that fit those phonetic sounds, such as TURTLE-PINOCHLE-MALL, and then link them to 0. If your link for 0 is SAW, then you would use the Link System to picture yourself using a saw to cut open a turtle who is playing pinochle at the mall. The next 10 digits (8979323846), would then be linked to 1 in the same manner.

To break the aforementioned world record, you would need to make links for every number from 0 to 8343, giving you 83,440 total memorized digits.

If you're asked to recall an individual digit at a certain point, you can do so if you've memorized enough digits with this system. For each set of 10 numbers memorized, consider the first number in the set as "digit 1". The second digit would be "digit 2", and so on, all the way up to "digit 10". If you want to know the 17,951st digit of Pi, you simply think about the set of 10 digits you've associated with the number 1795, and recall "digit 1" (the first digit). To find out the 2450th digit, you would recall which 10 digits you associated with 244, and recall "digit 10" (the last digit).

Thanks to the ability to recall every single digit, you will be able to restart from anywhere, should you make allowable mistakes in your record attempt. This particular method also makes it easy to memorize additional digits, should your record ever be broken. Thanks to the 10,000 mental pegs that SEM Cubed gives you, you can potentially memorize up to 100,000 digits of Pi!

discussion

pi day is March 14 ("3.14"), Albert Einstiens birthday (1879).

pi Approximation Day is on the 22/7 - that is, July 22. For the past few years, people at Chalmers University have celebrated it.

e approximation day is 19/7 -- that is, July 19.

Knowing what pi is, and knowing the first few digits of pi, is useful in carpentry, surveying, engineering, and many other fields. I use the ratio 355/113. I'd be very interested in any application of pi that needed more precision that that (needed more than 6 decimal places of precision). Other than, of course, showing off memory techniques. -- -- DavidCary? [[DateTime?(2005-02-26T21:20:49Z)]]

Should I mention something here about how to calculate pi from scratch -- rather than relying on other people's lists of digits? Physical methods measuring real (circular) objects generally only give 2 or 3 digits. -- -- DavidCary? [[DateTime?(2005-02-26T21:20:49Z)]]

Please don't add copyrighted material to the Mentat Wiki unless you're releasing it under the GnuFreeDocumentationLicense. -- Ron Hale-Evans [[DateTime?(2007-04-04T01:47:33Z)]]

Thanks for changing the embedded poems to links! -- Ron Hale-Evans [[DateTime?(2007-04-13T23:47:30Z)]]

Other Pi Memorization Resources

• 400-digit Pi Quiz: A javascript quiz for up to 400 digits of Pi
• Olle's Pi Page: A page where y ou can see how your memory of Pi ranks against others
• Pi World Ranking List: A page where you can see how your memory of Pi ranks against others
• pi mnemonics
• Cow-Pi Trainer: A web based pi memorization trainer. Start at any digit, get hints, compare your score to others.
• Wikipedia: pi day
• Wiki:ValueOfPi?