Let ε < 0.

03.14.09

Slices of pi

Filed under: Academic humor, Harmonic analysis — Travis @

Let’s take a quick break from the riddles and do a little something in celebration of Pi Day. To honor this most famous of the transcendental numbers, I’ve included a number of favorite pi mnemonics for your personal edification.

Pi mnemonics

There is in mathematical circles (ha!) a great and lengthy tradition of making mnemonics to memorize the digits of pi:

pi = 3.14159 26535 89793 23846 26433 83279 502….

In a traditional pi mnemonic, such as the one above, the number of characters in each word is used to represent a digit of pi, with the ocassional 10-, 11-, 12, or 14-digit word denoting two digits of pi. Punctuation is ignored. A famous example is the following:

God! I need a drink –
Alcoholic, of course –
After all those lectures
Involving radical equations.

Below are several more examples, listed in order of increasing decimal precision.

3.1416

May I draw a circle?
– Anon, found in Dmitri Borgmann’s Language on Vacation, 1965

Yes, I have a number.

– H. E. Licks, Recreations in Mathematics, 1917

3.14159

Wow, I made a great discovery!
–Anon

3.14159 2

Now I need a verse recalling pi.
–Irene Fisher & Dunstan Hayden, Geometry, 1965

3.14159 265

How I wish I could enumerate pi easily today.
–Anon

Yes, I know I shall recollect my number right.
–Wallace Lee, Math Miracles, 1960

May I draw a round enclosure as circle known?
–Dmitri Borgmann, Language on Vacation, 1965

3.14159 26535

May I have a large container of coffee, sugar and cream?
Anon

3.14159 26536 (rounded)

But I must a while endeavour
To reckon right the ratios.
–Anon, Mathematical Gazette, vol. 10, October 1921

3.14159 26535 8

Sir! I send a rhyme excelling
In sacred truth and rigid spelling.
–F. R. S., Nature, vol. 72, no. 1875, October 1905

3.14159 26535 8979

The mathematician’s version:
God! I need a drink –
Alcoholic, of course –
After all those lectures
Involving radical equations.
–Anon

The physicist’s version:
How I want a drink,
Alcoholic of course,
After the heavy chapters
Involving quantum equations.
–Sir James Jeans, c. 1932

3.14159 26535 89793 2384

Now I have a score notations
Of digits large and small,
teaching diameter’s precise relations,
And we can remember ‘tall.
–G. E. Gude, Scientific American Supplement, vol. 77, no. 1994, March 1914

3.14159 26535 89793 23846

How I wish I could recollect pi.
Eureka! cried the great inventor.
Christmas pudding, Christmas pie
Is the problem’s very center.
–Anon, found in Alan D. Baddeley’s The Pyschology of Memory, 1976

Now I sing a silly roundelay
Of radical roots, and utter “Lackaday!
Euclidean results imperfect are, my boy…
Mnemonic arts employ!”
–Willard R. Espy, An Almanac of Words at Play, 1975

3.14159 26535 89793 23846 264

Now I know a spell unfailing,
An artful charm, for tasks availing,

Intricate results entailing.
Not in too exact a mood…
(Poetry is pretty good!)
–Anon, Nature, vol. 72, no. 1878, October 1905.

How I want a drink,
Alcoholic of course,
After the heavy chapters
Involving quantum equations.
All of thy geometry,
Herr Planck, is fairly hard.
–Anonymous extension to Sir Jeans’ famous mnemonic above.

3.14159 26535 89793 23846 26433 8

For circumscribing a round enclosure or circle, every man
might remember ingenious numbers measuring one by one
diameter into circle or circle upon its own diameter…
–Anon, Mathematical Gazette, vol. 4, no. 65, July 1907.

3.14159 26535 89793 23846 26433 83279

See, I have a rhyme assisting
My feeble brain, its tasks sometime resisting,
Efforts laborious can by its witchery
Grow easier, so hidden here are
The decimals all of circle’s periphery.
–L. R. Stokelbach, The Scientific American Supplement, no. 1994, March 1914.

Now I — even I — would celebrate
In rhymes unapt, the great
Immortal Syracusan, rivaled nevermore
Who in his wondrous lore
Passed on before,
Left men his guidance how to circles mensurate.
–Adam C. Orr, Lierary Digest, vol. 32, no. 3, January 1906.

Now I will a rhyme construct,
By chosen words the young instruct,
Cunningly devised endeavors
Con it and remember ever
Widths in circle here you see
Sketched out in strange obscurity.
–Anon, The Dark Horse, 1951.

3.14159 26535 89793 23846 26433 83279 5

Sir: I wish I could recapture my memory about Sir
Jeans’ diabolic mnemonics! However, invention
now of any reliable easy phrase is beyond what shy
and fumbling aid my present intellect gives.
–Bill Powers, found in Willey Ley’s The Borders of Mathematics, 1967.

May I have a month, professor,
To figure these, you brain assessor?
Calculate, student, calculate now!
As the figuring gets longer,
My friend, hope you get stronger
And no figures incorrect allow!
–Aaron L. Buchman, School Science and Mathematics, 1953.

You I sing, O ratio undefined
By strict assay and lined,
Sequence limitless. Stunned regarding you,
We see eternity — alas — unwind
In random cast and rue,
Dejected out of measure, reckoning blind.
–John Freund, The Mathematics Teacher, vol. 62, 1969.

May I tell a story purposing to render clear
the ratio circular perimeter-breaths, revealing
one of the problems most famous in modern days,
and the greatest man of science anciently known.
–C. J. Jackson, Mathematical Gazette, vol. 4, 1907.

3.14159 26535 89793 23846 26433 83279 50288 41971 … (3835 digits!)

Of course, the all out winner, a massive mnemonic encoding 3835 digits of pi, is Michael Keith’s Cadaeic Cadenza, a fourteen chapter collection of digit-mindful paraphrasings of entire works of literature, including Edgar Allan Poe’s The Raven, Shakespeare’s Hamlet, Lewis Carroll’s Jabberwocky, and Carl Sandburg’s Grass, among others. Not only does he manage to preserve the story, structure, and rhyme schemes of these works, but Keith additionally encodes further pi mnemonics within the text itself. For example, the twelfth chapter includes an acrostic which itself encodes the digits of pi based on standard alphabetical number assignments. While absolutely useless in helping one recall the expansion of pi, it’s a breathtaking piece of mathematical and linguistic art.

Other useful ways to approximate pi

Archimede’s estimate: 22/7
This gives 3.14.

Chinese estimate: 335/113
This gives 3.141592, and can itself be rememebered as “1-1-3-into-3-5-5,” with pairs of the first three odd numbers.

And, of course, God’s estimate: 3
Really! Check out 1 Kings 7:23, or 2 Chronicles 4:2.

Pi limericks

‘Tis a favorite project of mine
A new value of pi to assign.
I would fix it at 3
For it’s simpler, you see,
Than 3.14159…

If inside a circle a line
Hits the center and goes spine to spine
And the line’s length is d
the circumference will be
d times 3.14159…

One last thought

Now I need a drink –
Alcoholic, of course –
After all these snippets
Involving precise mnemonics.
–Travis, Pi Day 2006

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