Cimarron County, Oklahoma, is the only county in the United States that borders four states (Colorado, Kansas, New Mexico, and Texas).
It’s also the only U.S. county to border six counties in five different states (two in Texas and one each in Colorado, Kansas, New Mexico, and Oklahoma).
When David Huffman died in 1999, the world lost a talented computer scientist — Huffman was best known for discovering the Huffman coding technique used in data compression.
But it also lost a pioneer in mathematical origami, an extension of the traditional art of paper folding that applies computational geometry, number theory, coding theory, and linear algebra. The field today is finding wide application, helping researchers to fold everything from proteins to automobile airbags and space-based telescopes.
Huffman was drawn to the work through his investigations into the mathematical properties of “zero curvature” surfaces, studying how paper behaves near creases and apices of cones. During the last two decades of his life he created hundreds of beautiful, perplexing paper models in which the creases were curved rather than straight.
But he kept his folding research largely to himself. He published only one paper on the subject (PDF), and much of what he discovered was lost at his death. “He anticipated a great deal of what other people have since rediscovered or are only now discovering,” laser physicist Robert Lang told the New York Times in 2004. “At least half of what he did is unlike anything I’ve seen.” MIT computer scientist Erik Demaine is working now with Huffman’s family to recover and document his discoveries (PDF).
“I don’t claim to be an artist. I’m not even sure how to define art,” Huffman told an audience in 1979. “But I find it natural that the elegant mathematical theorems associated with paper surfaces should lead to visual elegance as well.”
In the runup to Thailand’s 2001 elections, Thai Rak Thai party founder Thaksin Shinawatra faced allegations of corruption. The Bangkok Post‘s “week in review” email examined the charges against him, his attempts avoid the media, his reputation, and the Internet’s reaction. It used these paragraph headings:
Thaksin cited
Thaksin sighted
Thaksin slighted
Thaksin sited
In Indexers and Indexes in Fact and Fiction, Hazel K. Bell writes, “Clearly the editor is an indexer manqué.”
W. Langstaff offered this conundrum in Chess Amateur in 1922. White is to mate in two moves. He tries playing 1. Ke6, intending 2. Rd8#, but Black castles and no mate is possible. But by castling Black shows that his last move must have been g7-g5. Knowing this, White chooses 1. hxg6 e.p. rather than 1. Ke6. Now if Black castles he can play 2. h7#.
“Not so fast!” Black protests. “My last move was Rh7-h8, not g7-g5, so you can’t capture en passant.”
“Very well,” says White. “If you can’t castle, then I play 1. Ke6.” And we’re back where we started.
“What was really Black’s last move?” asks Burt Hochberg in Chess Braintwisters (1999). “If a position has a history, it can have only a single history, and Black would not be able to choose what his last move was any more than I can choose today what I had for dinner last night.”
“This is not a real game, however, but a problem in chess logic. The position’s history does not exist in actuality but only as a logical construct.”
aeolistic
adj. long-winded
[Edmund] Falconer’s Oonagh, or, The Lovers of Lismona opened one evening in 1866 at half-past seven. By midnight most of the audience had left; by two o’clock in the morning only a few sleeping critics were still there. At three o’clock the stage crew brought the curtain down with the action still in progress and the play was taken off.
— The Methuen Drama Dictionary of the Theatre, 2013
Here’s another interesting source of complementary sequences. Take any positive irrational number, say 
1 + X ≈ 2.4
1 + Y ≈ 1.7.
Now make a table of the approximate multiples of 1 + X and 1 + Y:
If we drop the fractional part of each number in the table, we’re left with two complementary sequences — every number 1, 2, 3, … appears in one sequence or the other, but never in both.
They’re called Beatty sequences, after Sam Beatty of the University of Toronto, who discovered them in 1926. A pretty proof by A. Ostrowski and J. Hyslop appears in the March 1927 issue of the American Mathematical Monthly and in Ross Honsberger’s Ingenuity in Mathematics (1970).
If box-office receipts are adjusted for inflation, Gone With the Wind is still the highest-grossing film of all time, with earnings of $3.4 billion in 2014 dollars.
After the film’s 1939 premiere in Atlanta, playwright Moss Hart wired producer David O. Selznick:
OH, ALL RIGHT, GO AHEAD AND HAVE A VULGAR COMMERCIAL SUCCESS!
During the American Civil War, enemy soldiers would sometimes meet to barter. Tobacco was hard to get in the North, and coffee was scarce in the South, so, where it could be done safely, soldiers would meet between the lines to trade.
In some cases this was done across distances. If a river or lake separated the lines, a tiny boat would be laden with commodities and sent to the other side, where it would be unloaded and filled with exchange cargoes, as agreed on by shouting and signaling across the water. On the Rappahannock early in 1863 a group of New Jersey soldiers received a shipment “by miniature boat six inches long.” It carried this note:
Gents U.S. Army
We send you some tobacco by our Packet. Send us some coffee in return. Also a deck of cards if you have them, and we will send you more tobacco. Send us any late papers if you have them.
Jas. O. Parker
Co. H. 17th Regt. Miss. Vols.
Alfred S. Roe, who served in a New York artillery unit, recalled that near Petersburg in the winter of 1864, “a certain canine of strictly impartial sentiments” was “taught to respond to a whistle from either side. Thus with a can of coffee suspended from his neck he would amble over to the Johnnies, and when they had replaced coffee with tobacco he would return in obedience to Union signals, intent only on the food reward both sides gave him.”
(From Bell I. Wiley, The Life of Billy Yank: The Common Soldier of the Union, 1952.)
“Faced with the choice between changing one’s mind and proving that there is no need to do so, almost everyone gets busy on the proof.” — John Kenneth Galbraith
In 1939, an ocean liner carrying 900 Jewish refugees left Nazi Germany seeking sanctuary in North America, but it was turned away by every nation it appealed to. In this week’s episode of the Futility Closet podcast we’ll follow the so-called “voyage of the damned” and the plight of its increasingly desperate passengers.
We’ll also discuss the employment prospects for hermits in Seattle and puzzle over the contentment of a condemned woman.