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SCENE: M.A.A. STUDENT CHAPTER MEETING, sparcely populated by STUDENTS and PROFESSORS.  Student president BEN, seated at the front of the room, is inexplicably wearing a faded tee-shirt that reads “COLLEGE MOM.”  TRAVIS, a professor, is among the group.

BEN:  I hope everyone had a good Pi Day yesterday.

The STUDENTS and PROFESSORS murmur assent.

BEN:  Any ideas on what we should do for Pi Day next year?

TRAVIS:  No, but I would like to propose that we set aside the day after, March 15, to celebrate the square root of minus one.

BEN:  March 15?

TRAVIS:  Yeah.  I figure we can call it the “i’s of March.”

(Pause.)

The STUDENTS groan collectively.

BEN:  Oh man, that’s terrible.  Just terrible.

TRAVIS:  I’m not taking abuse from a guy in a tee-shirt that says COLLEGE MOM.

(Pause.)

BEN: Et tu, Brutus?

Happy Pi Day! (That’s 3.14 to youse non-math typeses.) To honor this most famous of the transcendental numbers, I’ve included a number of favorite pi mnemonics for your personal edification.

“Pi mnemonics?” you say. “What are such things?”

Allow me to present an example

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

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.

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

T. Komplexify
Weizguyy Institute of Smart Axes

Abstract

In this article, we discuss the classic proof that girls are evil. The author will briefly discuss the origins of the problem and review the classic proof. The author then indicates a mathematical flaw in the argument, invalidating the statement. The article concludes with a revised and corrected statement of the result.

I. Introduction

I recently received an email discussing the differences between men and women from various mathematical and engineering points-of-view. Most of it was extremely funny, and sooner or later all shall certainly appear within the mathematico-humorist community, properly researched, and appended with standard references in the literature.

However, one portion of the email included a mathematical “proof” of the fact that girls are evil. This proof is doubtless familiar to many readers, having circulated a few times in mathematicians’ inboxes. However, for those readers unfamiliar with this well-known proof, we present it now.

II. Statement and classical proof of result

Theorem. Girls are evil.

Proof. It is axiomic in all cultures that girls require both time and money, and any man with either a deficiency in available “quality time” or “disposable income” knows that this a joint-proportion, whence

Similarly, it is has been proved that “time is money” [1], whence

Substitution yields

We also know that “money is the root of all evil” [2], whence

Substituting again yields

Squaring on the right-hand side of the equation yields

establishing the result. Q.E.D.

III. Identifying and resolving the flaw

The above “proof,” so-called, is widely known to mathematicians, leading to the widespread belief that girls are evil.

It will therefore come as a surprise to find that the proof above is flawed, and indeed, the result is incorrect. There is a subtle flaw in the above argument that seems to have escaped most diligent readers for quite some time. In the interest of correcting this mis-truth, which has improperly vilified girls as being evil, we present now the correct statement and its proof.

Theorem (Corrected). Girls are absolute evil.

Proof. Arguing as above allows us to conclude

However, let us more intently examine the consequences of money being the root of all evil. A moment’s thought shows that it is incorrect to conclude that

To see this, recall that evil is a inherently negative concept [3]. We cannot take square roots of negative quantities in the real world, lest we are will to assume that money is imaginary. (Graduate students in particular may choose to investigate this concept further [4].) Thus, we are therefore forced to conclude that

Substituting again yields

Squaring on the right-hand side of the equation yields

establishing that girls are absolutely evil. Q.E.D.

IV. Conclusion

We sincerely hope this clears things up.

V. Notes

1. I. Walker, “Time is money, professor proves,” CNN.com (2002) May 29
2. The Bible, King James Version (1611), I Timothy, Chapter 6, Verse 10
3. cf. Q. Smith, “An Atheological Argument from Evil Natural Laws,” (1991) Section 2.
4. This idea is explored somewhat in K. Marx, Das Kapital (1861).

The research reported in the paper has in part been suppressed by the National Silence Foundation.

This morning at work I stopped by the department office to check on any last-minute homework submissions and to say hi to our department secretaries, Laurie and Ginny.  On the front corner of Laurie’s desk sat a small plastic bowl filled about one third the way up with bright green Nerds.

No, not those Nerds.

You know, Nerds.  The Wonka brand of hard candy, consisting of a mass of tiny, crunchy globules of pure sugar with a slightly tart taste.  Imagine mating SweetTarts candy with, say, driveway gravel and you have the general idea of Nerds.  Now, despite this culinarily repugnant description, Nerds are one of my favorite candy treats: you can’t get anything more sugary than clumps of crystallized sugar, except possibly raw sugar itself.

Candy on Laurie’s desk is something of a common occurance.  Heck, it’s better than a calendar, actually, as Laurie rotates the candy treats in accordance with the appropriate seasonal activities: during October there’s candie corn, during December there’s gummy Christmas trees, during February there’s those little candy hearts made of old blackboard chalk, and so on.  What with St. Patrick’s Day just around the corner, a bowl of green Nerds seemed fittingly appropriate.

“Hi Laurie!” I said, before grabbing a handful of Nerds and popping them in my mouth.

At that point Laurie made a funny face, quite possibly in response to mine.  I had expected a blast of face-puckering tartiness, but instead was assaulted by what might most graciously be described as “fertilizer.”  My eyeballs rolled around in my head while my tongue tried to remove itself from the offending edibles by leaping out of my skull.

“Ugh! Laurie, those Nerds taste like shit!”

“No doubt.  They’re plant food.”

I try to walk to work whenever I can, partly because the four-mile walk is pretty good exercise, but mostly because it gives me fifty minutes of uninterrupted music.  South Dakota is, surprisingly, not a hotbed of industrial-gothic-EBM counterculture, so my mornings spent with me and my MP3 player are the closest I get to clubbing these days.

The selection of songs for each walk, made courtesy of my Rio’s “shuffle” feature, varies dramatically in quality from day to day, which I suppose is not surprising given the quantitiy of songs from which it may select.  Many days it feels as though the software designers were unclear as to the finer points of shuffleometry, as the MP3 player decides to simply play song after song after song from, say, the exact same album or artist.  Or in extreme cases, the exact same song over and over again (albeit, different remixes).

Such seemingly statistically anomalous events, when they occur, invariably turn my thoughts to Rosencrantz and Guildenstern Are Dead — perhaps my favorite play of all time, and certainly my favorite work by Tom Stoppard — from which I mentally paraphrase a list of possible explanations, which include:

Time has stopped dead, and the single experience of one track being played once has been repeated ninety-times. On the whole, doubtful.

and

A spectacular vindication of the principle that each individual song slected individually is as likely to be chosen as any other song, and therefore should cause no surprise each individual time it does.

and concluding with

One, probability is a factor which operates within natural forces. Two, probability is not operating as a factor. Three, we are now being held within un-, sub-, or supernatural forces.

I do like the idea of un-, sub- or supernatural forces being behind my music selection.

Anyhow, for every head-scratching choice made by the “shuffle” feature, there is also a sparkling gem of a playlist conceived via this technologically arbitrary process. Today’s was, in particular, a good’un:

1. Fictional: On Helloween
2. Toy: Charisma she said
3. Epsilon minus: Freedom (restriction)
4. Neuroticfish: Mechanic of the sequence
5. Hyperdex-1-sect: Les amants
6. Franka Potente: Wish (Komm Zu Mir)
7. Josh Wink: Higher state of conciousness (higher stated)
8. Assemblage 23: Anthem (exodus)
9. Razed in black: Visions (reprise)
10. Statemachine: Comprehensive

I’m not sure what it says when random chance can pick a better track listing for a mix CD than I can, but I’d like to think it’s because the un-, sub-, or supernatural forces all dig electro music.