How to memorize Pi
About 10 years ago we had an unofficial Pi Recitation Contest in school.
Somebody started to impress his friends with about 20 digits of Pi which he could
recite from memory. This ignited the competitive spirit of the whole class, and everyone
learned Pi now trying to be better than the others. Some months later, everyone in our class
knew at least 50 digits. I got up to 150 digits until the enthusiasm for Pi in our class
disappeared.
Then on March 7, 1995 I discovered Brendhan Givens' Pi Recitation Contest
on the Web and was very impressed by Eve Andersson's 251 digits. However, I decided to break
her record. Two weeks later I could recite 302 digits, when Antranig Basman appeared. We both
wanted to be the best, so in the following days we fought a little battle. The current score
was
911:901
digits for Antranig Basman when the contest ended. :-(
By the way, Antranig and me both had luck anyway, because
Olle Windelius
had submitted a whole lot more digits, but hit a wrong key at position 762,
the last digit before the Feynman Point where six nines occur in a row.
You wonder how I could memorize 900 digits of Pi?
(By the way: Now I can recite 1500.) Well, maybe it is easier than you think...
The two basic techniques
The fixed-length method
Here you divide the digits into groups of a fixed length, e.g. five
(3. 14159 26535 89793 23846...), and then learn these groups like telephone numbers.
Eve Andersson and
Stefan Sarstedt
use this technique with length seven, Olle Windelius with length five.
I myself used this method in school (with length three),
therefore I still use it for the first 150 digits.
The advantage of a short length is that it is easier to memorize a single group. The advantage
of a long length is that as the number of groups to learn is smaller errors like accidentally
swapping two groups or leaving out one will occur not as often.
The variable-length method
In my opinion this is a more efficient technique.
Here you split the digits in a way that enables you to memorize them as easy as possible.
The first thing to do when you learn a new block of digits is to look carefully at the
numbers and search for patterns, e.g. palindrome numbers, groups that occur twice or more,
year numbers, poems (number groups that rhyme), numbers with repeating digits or whatever
comes to your mind.
Have a look at the digits 151-180. Imagine you want to memorize them all.
481117450284102701938521105559
Which digits are the easiest? I think it's 111 and 555. Now we splitted one big problem
into five smaller ones:
48 - 111 - 745028410270193852110 - 555 - 9
It starts with 48, then comes the first easy number 111, then a medium problem, then the
second easy number 555 and finally it ends with a 9.
Now analyze the "medium problem": 745028410270193852110
I splitted it the following way:
7450..28410..270 - three groups ending with 0
1938............ - a year number
52.............. - the number of weeks in a year
110............. - the emergency telephone call (in Germany)
The main problem is to find patterns and divide the digits into the right groups.
Then memorization can be done in very little time. Try it out!
My own technique
Digits 0-22 : Rebecca Brannon's Poem
I think this poem is a good start for memorizing Pi.
It fits the tune of "America" from West Side Story:
three point one four one five nine
two six five three five eight nine
seven nine three two three eight four
six two six and a whole lot more.
Digits 13-30 : The Giant Palindrome
If you use only the first two lines of the poem (digits 0-12), you can memorize the
digits up to position 30 in the following way:
79...........
..32.........
....38.......
......46264.3 - If you disregard the 3, the center of the palindrome is a palindrome itself
....38.......
..32.........
79...........
Digits 31-60
50 288 419 716 93993 7510 5 820 974 944
Don't ask me why I splitted the digits this way. I can't remember it.
Digits 61-150
Fixed-length method, length=3
592 307
816 406 286 - notice the suffix 6
208 998 628 - notice the suffix 8
034 825
342 117 067 982 148 086 513 282 306 647
093 844 609 550 582 231 725 359 408 128
I wouldn't say that this is the best way. I just didn't know anything better when I
learned these digits.
Digits 151-180
Already mentioned above.
Digits 181-240
6446......... - a palindrome number starts the first half of the block
229..489..549 - three 3-groups ending with 9
30..38....... - two 2-groups starting with 3
1964..4...... - a year and a month
288..1097.... - end of first half
5665......... - a palindrome number starts the second half of the block
933 446...... - three odd and three even numbers
128 475...... - a power of 2, a multiple of 25
Now comes a little poem:
648..233.....
786..783..... - Intel's next processor? (786)
165.......... - end of block
Digits 241-300
271....... - the number e starts with 2.71...
20........ - easy to memorize anyway
1909..1... - a year and a month
456..4856. - three increasing digits, then the same again with inserted 8
69..23..46 - three multiples of 23, or 69-23=46
03486..... - sounds like a name for a processor
104.......
5432..66.. - four decreasing digits and then a higher digit twice
4821...... - a permutation of the geometric series 1,2,4,8,...
3393...... - 3+3=9-3
60..72..60 - a shoulder-head-shoulder constellation
249.......
141....... - the square root of 2 starts 1.41...
273....... - the first number of the block +2
Digits 301-360
724..587.......
00..66..06..... - twice 0, twice 6, once 0, once 6
3155...........
881..74..881..5 - notice that 881 occurs twice
209..209....... - twice 209
6..............
28..29..25..... - three numbers starting with 2
409............ - similar to the 209 before
171............ - a palindrome number
536..436....... - two similar numbers
789............ - three increasing digits
2590..360...... - two numbers ending with 0
Digits 361-420
011................... - the emergency call backwards
3..305..305........... - Unit 305 is Germany's best Tank Artillery Bataillon
488..20..466..........
521..3841..46.........
951..941..511..60..943
305................... - Unit 305 again
727................... - Boeing 727
0.....................
365................... - the number of days in a year
759591953............. - a melody of odd numbers
Digits 421-480
09..2..18..6117 - 09 * 2 = 18, suffix 6117
381..932...6117 - suffix 6117 again
931 0511....... - 931 is clawed back from 932, both groups end with 1
85480..........
744............
6237..99..627.. - consider 99 as an operator that eliminates the 3 in 6237
49..567........ - the square of 7, three increasing digits ending with 7
351..885.......
752..724....... - prefix is 7, block ends like the 6th block (301-360) began
Digits 481-540
This is one of the most beautiful blocks. Besides it's the first block where I began using overlapping
patterns.
Main Structure
89122793818301194912983..................................... - The Opening Poem
......................33673362.............................. - First Sequence
.............................24406566430860................. - Second Sequence
...........................................21394946395224... - The Closing Poem
.........................................................737 - Boeing 737 Finale
Opening Poem
89'1 22'7 93'8 18'3 (the last digit of each group is stressed)
01 1949 12983...... (read as 'o one 'nineteen 'forty-'nine 'one two 'nine eight 'three)
First Sequence
3367..3362 - this is straight-forward: prefix is 336
Second Sequence
2440....
65..66.. - the counting
430..860 - the doubling
The Closing Poem
213..94..94 - last digit is stressed each time
639..52..24 - notice that 639 is a multiple of 213
Digits 541-600
19070217.................................................... - 1907 Feb 17
........9860943............................................. - Intel 986
...............702770....................................... - Pause
.....................53921717629317......................... - Main Sequence
...................................675238................... - Pause
.........................................4674818467......... - The Sandwich
...................................................669405132 - Closing Sequence
Main Sequence
5392..17..17
6293..17
The Sandwich
467..4818..467
Digits 601-660
0005681271452635608......................................... - Opening Sequence
...................277857713427577.......................... - Suffix 7 Sequence
..................................896091.................... - Pause
........................................736371787214........ - Prefix 7 Sequence
....................................................68440901 - Closing Sequence
Suffix 7 Sequence
277..8..577..13427..577
Prefix 7 Sequence
7363..7178..7214
Digits 661-720
2249534301465495853.........................................
...................710507922796............................. - Prefix 7
...............................89258923..................... - Need I say more?
.......................................5420199561121........
....................................................29021960 - Leap Day 1960
Digits 721-780
86403441815981362977477130996051870721134...................
.........................................999999............. - The Feynman Point
...............................................8372978049951
Digits 781-1200
And so on...I think you have understood the idea.
059731732816096318595024459455346908302642522308253344685035
261931188171010003137838752886587533208381420617177669147303
598253490428755468731159562863882353787593751957781857780532
171226806613001927876611195909216420198938095257201065485863
278865936153381827968230301952035301852968995773622599413891
249721775283479131515574857242454150695950829533116861727855
889075098381754637464939319255060400927701671139009848824012
Digits 1201-1500
At location 1200 I switched from my weird 60-blocks to 50-blocks.
By the way, Stefan Sarstedt uses 49er-blocks. =)
85836160356370766010471018194295559619894676783744
94482553797747268471040475346462080466842590694912
93313677028989152104752162056966024058038150193511
25338243003558764024749647326391419927260426992279
67823547816360093417216412199245863150302861829745
55706749838505494588586926995690927210797509302955
Digits 1501-6000
Don't ask me. Ask
Olle.
Digits 6001-40000
Ask Hiroyuki Goto.
Digits 40001-infinity
Hell no! Can you never get enough?
Further techniques
In the last days of the contest I have experimented with overlapping patterns.
Example (digits 665-678): 53430146549585
My technique to memorize this is:
53 43............ two similar numbers
....3014......... like the beginning: 3.14 (consider 0 as .)
.......465 495... again two similar numbers
............95 85 and again
The advantage of this technique is that the last digit of a pattern gives you
a hint which pattern comes next.
Here is a fantastic program that will help you with your training:
Stefan Sarstedt's
PiTrainer.
The program needs a file pi.txt which was created by
Roy Williams'
program to compute Pi.
Here is Antranig's fantastic
Guide to the first 1000 digits of Pi.
And here is
Olle's technique.
Since he knows 6000 digits, this must be the most efficient one.
If you need some motivation while
you are trying to memorize hundreds of digits, remember this.
Last updated February 6, 1997
Mark Dettinger