Mnemonic

This French alexandrine encodes π to 126 decimal places:

Que j’aime à faire apprendre un nombre utile aux sages!
Immortel Archimède, artiste ingénieur,
Qui de ton jugement peut priser la valeur?
Pour moi, ton problème eut de pareils avantages.
Jadis, mystérieux, un problème bloquait
Tout l’admirable procédé, l’œuvre grandiose
Que Pythagore découvrit aux anciens Grecs.
Ô quadrature! vieux tourment du philosophe!
Insoluble rondeur, trop longtemps vous avez
Défié Pythagore et ses imitateurs.
Comment intégrer l’espace plan circulaire?
Former un triangle auquel il équivaudra?
Nouvelle invention: Archimède inscrira
Dedans un hexagone; appréciera son aire,
Fonction du rayon. Pas trop ne s’y tiendra:
Dédoublera chaque élément antérieur;
Toujours de l’orbe calculée approchera;
Définira limite; enfin, l’arc, le limiteur
De cet inquiétant cercle, ennemi trop rebelle!
Professeur, enseignez son problème avec zèle!

Translation:

How I like to teach this number useful to the wise.
Immortal Archimedes, artist, engineer,
In your opinion who could estimate its value?
For me, your problem had equal advantages.
Long ago, mysterious, a problem blocked
All the honorable process, the great work
That Pythagoras revealed to the Ancient Greeks.
Oh quadrature! Old philosopher’s torment
Unsolvable roundness, for too long you have
Defied Pythagoras and his imitators.
How to integrate the plain circular space?
Form a triangle to which it is equivalent?
New invention: Archimedes will inscribe
Inside a hexagon; will appreciate its area
Function of a ray. Not too much to hold onto there:
Will split each previous element;
Always the calculated orb will approach
Will define the limit; finally, the arc, the limiter
Of this disturbing circle, an enemy too rebellious
Teacher, teach its problem with zeal.

I don’t know who came up with it — Alfred Posamentier traces it as far back as the Nouvelle Correspondence Mathematique of Brussels, 1879.

May 23, 2018May 23, 2018 | Poems · Science & Math

Unfinished

A puzzle by David L. Silverman:

On the back of an envelope you find an interrupted game of tic-tac-toe (noughts and crosses). You know that each player was an expert, which means that she never puts herself into a potentially losing position and that she always wins if her opponent gives her the opportunity. There are two Xs and two Os in the diagram, and it is impossible to tell whose move it is. Neglecting symmetry, what is the position?

	Select Click for Answer
This solution is by Clayton W. Dodge of the University of Maine at Orono: Number the boxes 1-9 from top left to lower right, so that the first column is 1-4-7. Now: 1. The middle box must be empty. If it were marked, say with an X, then the board’s second X would have to be adjacent to it somewhere, and an O must complete that row, column, or diagonal. But now wherever we place the remaining O, the O player can immediately force a win by making a double threat if she has the move. X would be guilty of malpractice for allowing this disaster to come about, and we know she’s an expert player. So it must be X’s turn to move. But now we’ve deduced whose turn it is, and we’ve been told this is impossible. So this whole scenario cannot be the case — the center box must be empty. 2. No two similar marks can appear symmetrically around box 5, since then (if that player has the move) it leads to an immediate win or (if that player doesn’t have the move) we’re violating observation 1 above. 3. The same mark, say X, can’t appear in two adjacent corners, because then an O must appear between them, as well as in another box that will allow O to make two simultaneous threats if she has the move. 4. The same mark, say X, can’t appear in two middle-of-an-edge squares. If Xs appeared in, say, 2 and 8 we’d be violating observation 2. If they appeared in boxes 2 and 4, then one O must go in box 1 (to prevent the double threat) and another in box 6 or 8 to prevent X from winning with box 5. But then O can win with box 9. 5. The same mark, say X, can’t occupy two adjacent squares (say 1 and 2), since then an O must go in box 3 and another box that would allow O to make a double threat if she has the move. 6. Putting all this together, each player has marked one corner and one box opposite to it in the middle of an edge. There are four possibilities: If X has played to 1 and 6 and O to 2 and 9, then X can play to 4 and force a win. If X has played to 1 and 6 and O to 2 and 7, then X can play to 5 and force a win. If X has played to 1 and 6 and O to 4 and either 3 or 9, then expert play will always lead to a draw. So the envelope must bear one of these two diagrams (or its symmetrical counterpart): (From Pi Mu Epsilon Journal 5:10 [Spring 1974], 534.)

Click for Answer

This solution is by Clayton W. Dodge of the University of Maine at Orono:

Number the boxes 1-9 from top left to lower right, so that the first column is 1-4-7. Now:

1. The middle box must be empty. If it were marked, say with an X, then the board’s second X would have to be adjacent to it somewhere, and an O must complete that row, column, or diagonal. But now wherever we place the remaining O, the O player can immediately force a win by making a double threat if she has the move. X would be guilty of malpractice for allowing this disaster to come about, and we know she’s an expert player. So it must be X’s turn to move. But now we’ve deduced whose turn it is, and we’ve been told this is impossible. So this whole scenario cannot be the case — the center box must be empty.

2. No two similar marks can appear symmetrically around box 5, since then (if that player has the move) it leads to an immediate win or (if that player doesn’t have the move) we’re violating observation 1 above.

3. The same mark, say X, can’t appear in two adjacent corners, because then an O must appear between them, as well as in another box that will allow O to make two simultaneous threats if she has the move.

4. The same mark, say X, can’t appear in two middle-of-an-edge squares. If Xs appeared in, say, 2 and 8 we’d be violating observation 2. If they appeared in boxes 2 and 4, then one O must go in box 1 (to prevent the double threat) and another in box 6 or 8 to prevent X from winning with box 5. But then O can win with box 9.

5. The same mark, say X, can’t occupy two adjacent squares (say 1 and 2), since then an O must go in box 3 and another box that would allow O to make a double threat if she has the move.

6. Putting all this together, each player has marked one corner and one box opposite to it in the middle of an edge. There are four possibilities:

If X has played to 1 and 6 and O to 2 and 9, then X can play to 4 and force a win.
If X has played to 1 and 6 and O to 2 and 7, then X can play to 5 and force a win.
If X has played to 1 and 6 and O to 4 and either 3 or 9, then expert play will always lead to a draw.

So the envelope must bear one of these two diagrams (or its symmetrical counterpart):

(From Pi Mu Epsilon Journal 5:10 [Spring 1974], 534.)

May 23, 2018 | Puzzles

In a Word

bibliopolist
n. a bookseller

cunctative
adj. slow; tardy; dilatory; causing delay

numquid
n. an inquisitive person

aliunde
adv. from elsewhere; from another source

[Edmund Law] had a book printed at Carlisle; they were a long time about it: he sent several times to hasten them; at last he called himself to know the reason of the delay. ‘Why does not my book make its appearance?’ said he to the printer. ‘My Lord, I am extremely sorry; but we have been obliged to send to Glasgow for a pound of parentheses.’

— Henry Colburn, Personal and Literary Memorials, 1829

May 22, 2018 | Language · Literature

Rewrites

king kong

Edgar Wallace died after completing a rough draft of King Kong, and James Ashmore Creelman’s script was slow and dialogue-heavy. So Merian C. Cooper gave the job to Ruth Rose, the wife of his co-producer. Rose had never composed a script before, but she knew how to write tightly — the opening line of dialogue, “Hey! Is this the moving picture ship?”, replaces several pages of exposition with seven words. After Kong is subdued on Skull Island, she accomplishes his transfer to New York with a simple speech by filmmaker Carl Denham:

Send to the ship for anchor chains and tools. Build a raft and float him to the ship. We’ll give him more than chains. He’s always been king of his world, but we’ll teach him fear. Why, the whole world will pay to see this! We’re millionaires, boys — I’ll share it with all of you! In a few months it’ll be up in lights: ‘Kong, the Eighth Wonder of the World!’

Ernest B. Schoedsack said his wife’s script was easy to shoot because “the characters are believable — I didn’t have to ask them to do anything impossible or ridiculous.” And Cooper added, “Ruth used just the kind of romantic dialogue I wanted. It was perfect.”

May 22, 2018 | Entertainment

Podcast Episode 201: The Gardner Heist

In 1990, two thieves dressed as policemen walked into Boston’s Gardner museum and walked out with 13 artworks worth half a billion dollars. After 28 years the lost masterpieces have never been recovered. In this week’s episode of the Futility Closet podcast we’ll describe the largest art theft in history and the ongoing search for its solution.

We’ll also discover the benefits of mustard gas and puzzle over a surprisingly effective fighter pilot.

See full show notes …

May 21, 2018May 28, 2018 | Art · Crime · Podcast

Stairs of Knowledge

balamand stairs of knowledge

This staircase near the library at Lebanon’s University of Balamand is painted to resemble a stack of classic texts:

The Epic of Gilgamesh
The Republic of Plato
Diwān Abū al-Tayyib al-Mutanbbī
Risālat al-ghufrān / Abī al-Alā al-Ma’arrī
The Divine Comedy by Dante Alighieri
Muqaddimah-i ibn Khaldūn
The Prince and the Discourses by Niccolò Machiavelli
Discourse on Method by René Descartes
The Critique of Pure Reason by Immanuel Kant
Faust by Goethe
The Origin of Species by Charles Darwin
The Brothers Karamazov by Fyodor Dostoyevsky
Thus Spake Zarathustra by Friedrich Nietzsche
The Meaning of Relativity by Albert Einstein
The Prophet by Khalil Gibran
al-Ayyām / Tāhā Husayn
A Study of History by Arnold Toynbee
Cosmos by Carl Sagan
A Brief History of Time by Stephen Hawking
Les Désorientés by Amin Maalouf
The Road Ahead by Bill Gates

This puts them (almost) in chronological order.

May 20, 2018 | Literature

Circumstance

In the afternoon I went upon the river to look after some tarr I am sending down and some coles, and so home again; it raining hard upon the water, I put ashore and sheltered myself, while the King came by in his barge, going down towards the Downs to meet the Queen; the Duke being gone yesterday. But methought it lessened my esteem of a king, that he should not be able to command the rain.

— Samuel Pepys, diary, July 19, 1662

May 19, 2018 | Society

Leaps and Bounds

English cricketer C.B. Fry had a curious party trick: He would stand on the floor facing a mantelpiece, crouch, and leap upward, turning in midair and landing with his feet planted on the shelf, from which he would bow to onlookers. He claimed to be able to do this into his 70s.

On July 17, 1933, John Dillinger walked into the Daleville Commercial Bank in Indiana and told the teller, “Well, honey, this is a holdup. Get me the money.” Told there was no key to the teller’s cage, Dillinger vaulted over the counter himself to investigate. “This would become another of his well-known trademarks,” writes John Beineke in Hoosier Public Enemy, “the quick and graceful vaults over counters that were often several feet high. The feat earned him the nickname ‘Jackrabbit’ in some newspapers.”

In a letter to the Times on March 16, 1944, G.M. Trevelyan, the Master of Trinity College, Cambridge, remarks on the tradition of trying to leap up the eight semicircular steps of the college hall at one bound. “The only person to succeed of whom I know was the gigantic [William] Whewell, when he was Master of the college; he clapped his mortar-board firmly on his head, picked up his gown with one hand, and leapt.”

Trevelyan had recently learned that Henry Hutchinson Montgomery, later a bishop, had made the jump during his undergraduate career at Trinity, between 1866 and 1870, and “I have heard that the feat was accomplished once or twice in this century; once, I was told, an American succeeded, but I have not the facts or names. It has certainly been done very seldom.”

(Thanks, Chris.)

May 18, 2018 | Oddities

Progress

Georgia’s Savannah airport hit a delicate snag in the 1980s — a planned extension to Runway 10 was delayed because a local family refused to move the graves of Richard and Catherine Dotson, a farming couple who had been laid to rest in the land they’d cultivated for decades.

The solution was to pave over the graves but lay the two headstones in its surface. They read “At rest” and “Gone home to rest” — but there’s a legend among pilots that if you land just after sundown you’ll see two uneasy figures on the runway’s north side.

South Carolina’s newspaper The State notes, “Family members are still escorted to visit them safely, though they cannot leave flowers.”

May 18, 2018 | Death · Oddities

The Empty Set

Mathematician John Rainwater has published 10 research papers in functional analysis, notably in the geometric theory of Banach spaces and in convex functions. The University of Washington has named a regular seminar after him, and Rainwater’s Theorem is an important result in summability theory.

This is most impressive because he doesn’t exist. In 1952 UW grad student Nick Massey received a blank registration card by mistake, and he invented a fictional student, naming him John Rainwater because it was raining at the time. “Rainwater” was adopted by the other students and began to submit solutions to problems posed in the American Mathematical Monthly, and he’s gone on to a 60-year (so far) career of considerable distinction — his top paper has 19 citations.

Asked why he’d published that paper under Rainwater’s name, John Isbell quoted Friedrich Schiller: “Man is only fully human when he plays.”

May 17, 2018 | Oddities · Science & Math

An idler's miscellany of compendious amusements

Author: Greg Ross