Reader Éric Angelini points out that the regular continued fraction of 
- in numbers: 1, 10, 1, 10, 1, 10, …
- in English!: ONE, TEN, ONE, TEN, ONE, TEN, …
A simpler specimen: 9 9 9 9 … is NINE NINE NINE NINE …
(Thanks, Éric.)
For What It’s Worth
A 2009 study in the journal Sex Roles found that James Bond had had “strong” sexual contact with 46 women in the first 20 films in the Eon Productions Bond series (up to Die Another Day).
He had “mild” encounters, such as kissing, with another 52.
For comparison, Bond author Henry Chancellor had counted 58 sexual encounters in the first 20 films (according to Ben MacIntyre in For Your Eyes Only). Interestingly, Chancellor calculated that Bond sleeps with just 14 women in the 12 books that appeared between 1953 and 1964.
Still, that’s a lot of partners. “The likelihood of James Bond having chlamydia is extremely high,” general practitioner Sarah Jarvis told the BBC. “If he came to my clinic I would definitely advise him to have an STI test.”
(Kimberly A. Neuendorf, et al., “Shaken and Stirred: A Content Analysis of Women’s Portrayals in James Bond Films,” Sex Roles 62:11-12 [2010], 747-761.)
Elevenses
On a standard calculator keypad like the one shown here, any four-digit number that is typed in a rectangular shape is evenly divisible by 11. Some examples: 7964, 6523, 1793, 7128. (The numbers must not include 0.)
Parallelograms work too: 1562, 6875, 2783, etc.
Discussion and some proofs here.
09/20/2023 More: Take three digits in order from any row, column, or main diagonal and append the same three digits in reverse order (e.g., 951159). The resulting number will always be evenly divisible by 37 (and, indeed, by 1221). Mathematical Gazette, December 1986 and June 1987. See also A Keypad Oddity.
Four-Mile Fall
In January 1942, Soviet Air Force lieutenant Ivan Mikhailovich Chisov was serving as navigator on an Ilyushin Il-4 bomber when an attack by Messerschmitt fighters forced him to bail out.
He left the plane at 6,700 meters and decided to forgo opening his parachute until he’d dropped below the level of the battle. But due to the thin atmosphere he passed out before he could pull the ripcord.
At an estimated 200 kph he struck the edge of a ravine whose steep sides were covered in deep snow. He tumbled to the bottom, where cavalrymen found him alive and still wearing his unopened parachute. He spent a month in critical condition with a broken pelvis but was flying again three months later.
Play On
Local rules adopted at British golf courses during World War II:
- “In competitions, during gunfire or while bombs are falling, players may take cover without penalty for ceasing play.”
- “The positions of known delayed-action bombs are marked by red flags placed at a reasonably, but not guaranteed, safe distance therefrom.”
- “A ball moved by enemy action may be replaced, or if lost or destroyed, ball may be dropped not nearer the hole without penalty.”
- “A player whose stroke is affected by the simultaneous explosion of a bomb may play another ball from the same place. Penalty one stroke.”
In Curiosities of Golf (1994), Jonathan Rice writes, “At Folkestone GC, the wartime rules included the rather grudging allowance that ‘a ball may be lifted and dropped if in a bomb hole in the rough, but not if the bomb hole is in or part of a recognized hazard.’ So if you sliced your drive and just caught a bunker by the side of the fairway, which then turned out to be fifty feet deep thanks to an overnight bombing raid, you just had to play out of the hazard, however unrecognizable it might have been compared with the day before. They breed tough golfers in Folkestone.”
In July 1941, some American clubs reportedly adopted similar rules in a show of solidarity.
UPDATE: Here are the rules adopted by Richmond GC, southwest of London. (Thanks, Brieuc.)
Missed Connections
Nineteenth-century personal ads from the New York Herald:
WILL THE YOUNG LADY WHO ACCIDENTALLY fell while dancing at Barnum’s Museum, on Monday evening, address a note to Interested, Herald office, as a gentleman would like to make her acquaintance, if perfectly agreeable to her? (Jan. 22, 1862)
NIBLO’S, MONDAY EVENING — OCCUPIED adjoining seats in parquet; repeated pressure of arm and foot and hands met when separating. If agreeable, address Bruno, box 211 Herald office. (July 17, 1867)
“WON’T YOU LOOK IN THE HERALD TO-MORROW?” — Will the young lady to whom the above was addressed appoint an interview with the gentleman wearing eyeglasses? Address A.B., Station D. (Dec. 17, 1867)
WILL THE YOUNG LADY, WITH CURLS, WEARING a straw bonnet, and I think plaid shawl, and who carried a Herald in her hand, and who came down Park row to Broadway, and down Broadway to Dey street, turning into Dey street about 11 o’clock yesterday, and who in Dey street met and spoke to a gentleman and then went into a fur store in Dey street, near Greenwich, oblige the gentleman who stood on the opposite side of Dey street, as he very much desires an acquaintance? Address T., Herald office. (Feb. 18, 1862)
AN INTRODUCTION IS EARNESTLY SOLICITED OF the young lady or her friends or family, by the gentleman and his mother who stopped their carriage Friday morning to assist a young lady who had jumped from a stage she had just entered, corner 5th av. and 39th st., to rescue the old gentleman who had fallen in the roadway. The young lady is about 20 years of age and very beautiful; wears her hair in large brown waves; has rosy complexion and soft blue eyes; wore Persian gilt walking coat and muff. We desire her acquaintance and to present her in our family. Address MOTHER AND SON, Herald Uptown office. (Feb. 8, 1880)
(From Sara Bader, Strange Red Cow: And Other Curious Classified Ads From the Past, 2005.)
The Book of Truth
Once I read a book of 100 numbered pages with one sentence on each page. Page 1: ‘The sentence on page 2 is true.’ Page 2: ‘The sentence on page 3 is true.’ And so on to page 100: ‘The sentence on page 1 is false.’
On the second reading, page 100 changes the entire book. If page 1 is false, then the truth is ‘The sentence on page 2 is false.’ Likewise, page 2 becomes ‘The sentence on page 3 is false.’ And so on to page 100, which now should be read as ‘The sentence on page 1 is true.’
What happens on the third reading?
— David Morice, “Kickshaws,” Word Ways 26:1 (February 1993), 44-55. See Yablo’s Paradox.
Fore and Aft
Add the same three letters, in order, both before and after the following to make a familiar English word:
ERGRO
Pen and Ink
In 1980, after 30 years of drawing Beetle Bailey, comic artist Mort Walker published The Lexicon of Comicana, a lighthearted meditation on the many conventions that a reader of comic strips is expected to understand. He calls it a lexicon because he’s made up names for all of them:
- A grawlix (above) is a string of symbols representing profanity.
- Emanata are lines surrounding a character’s head to indicate surprise or shock.
- A lucaflect is the distorted image of a window in a shiny object.
- Blurgits are blurs of motion within a single panel, to denote frenzied action.
- Sphericasia are lines tracking motion: a throwatron is a line following a football, a sailatron follows a wandering paper airplane, and a dashed staggeratron follows an intoxicated person. If the motion is particularly fast, these might begin with a dust cloud, called a briffit.
- Plewds are flying droplets of sweat to indicate stress, hard work, or nerves.
- An indotherm is a series of wavy lines to indicate rising heat.
- Vites are fine vertical lines to indicate a shine on a floor. Strangely, a window or mirror bears dites, which are diagonal.
More: a light bulb represents an idea, Zs (or a saw cutting a log) represent snoring, distant birds are inverted Ws, patches denote poverty, all bones are the same shape, all new things have price tags, all injuries require bandages, all paint cans bear drippings. Who invented all these conventions, and how did we all learn to observe them?
Scratch
Can a chess knight visit every square on a board with 4 rows by a series of successive moves?
No, it can’t, and Hungarian mathematics prodigy Louis Pósa proved this while still in his early teens. Suppose that such a tour is possible. Then, on any board bearing the standard checkerboard pattern, the knight will land alternately on white and black squares. But now imagine that the board’s top and bottom rows have been colored red and the middle two rows are blue. Now a knight on any red square must jump to a blue square, and because the board has an equal number of red and blue squares, any knight on a blue square must jump to a red one (if it visits two blue squares in a row, it won’t be able to make up for this later by visiting two red ones in a row). So the knight’s tour on any 4 × n board must alternate strictly between red and blue squares.
“But this is impossible,” notes Colorado College mathematician John J. Watkins. “The same knight’s tour alternated between white and black squares in the one coloring, and between red and blue squares in the other coloring, which would mean the two color patterns must be the same, which of course they aren’t. Isn’t that a clever proof, especially for a teenager to discover?”
(John J. Watkins, Across the Board, 2004. Pósa’s proof is given more rigorously here, and it’s also presented in Ross Honsberger’s 1973 book Mathematical Gems.)
UPDATE: It’s important to note that it’s a “closed” knight’s tour that’s impossible — that’s one that ends where it began. An open tour, which can end anywhere, is possible — it breaks Pósa’s proof because it need not alternate strictly between red and blue squares. Thanks to reader Marjan Milanović for pointing this out.