Can a square be inscribed in any triangle?
Can a square be inscribed in any triangle?
In August 1891, a man named Frank Melbourne arrived in drought-stricken Cheyenne, Wyo., and claimed that he could summon rain at will. He proposed to produce rain within three days in return for a sizable fee.
“He established himself in the loft of a barn in the suburbs of the city and has been there ever since, except when leaving it for his meals,” reported the Rocky Mountain News. “The only apparatus or chemicals he took into his retreat were contained in four ordinary gripsacks. The windows of the barn were carefully shaded with blankets, and the crevices in the floor of the barn loft covered to prevent any eye penetrating the mystery of the rain-making laboratory.”
At first his efforts seemed to have no effect, but on the third day the sky darkened. “Business was almost suspended and thousands of people were on the streets watching the clouds. At 2:40 o’clock there was a heavy peal of thunder and a vivid flash of lightning, and in a few moments the rain came down in torrents.” Melbourne emerged and claimed credit; to convince skeptics, he returned to the loft a few days later, and again showers fell.
This established his reputation, and he moved on to Salt Lake City and Kelton, Utah, and Goodland, Kan., which were also suffering dry spells. He returned to Cheyenne the following summer, promising to cover 5,000 square miles with rainfall, but this time he produced only a few scattered showers. The committee refused to pay him, and he left Cheyenne for good.
Scientific American noted that Melbourne spent the years 1892 to 1894 aboard a specially rigged railroad car, offering his services to any community along the route. “So long as frequent rains occurred,” the editors observed, “although they were natural and were predicted by the Weather Bureau …, yet the farmers of Iowa, Kansas, and Nebraska, ignoring this fact, were sure to accredit all success to Mr. Melbourne.”
The Iowa Weather and Crop Service was more blunt. Melbourne ought to emulate the rain dancers of the Winnebago Indians, it said: “When they begin operations they never let up until it rains, so they score a success every time.”
“Terms of approbation and eulogy in American dialect speech,” compiled by Elsie Warnock for Dialect Notes, 1913:
“The facetious terms ‘gobsloptious,’ ‘gobersloptious,’ ‘globsloptious’ and ‘supergobsloptious,’ ‘superglobsloptious,’ ‘superglobbersloptious,’ and ‘supergobosnoptious’ seem to be variant forms differing because of the desire of one person to outdo another in the force of his terms of eulogy.”
By J. da C. Andrade, Empire Review, 1923. White to mate in two moves.
Letter to the Times, June 17, 1978:
It is not only dates that make nice patterns of numbers. Some years ago I was bringing a Destroyer home from the Far East and was required to report my position twice a day.
One evening, I saw that we would be passing close to where the Greenwich Meridian cuts the Equator so arranged to arrive there dead on midnight. Once there I altered course to due North and stopped engines so my position signal read:
At 0000 my position Latitude 00°00’N, Longitude 00°00’E. Course 000°. Speed 0.
I had considered saying I was Nowhere but thought (probably correctly) that Their Lordships would not be amused.
In October 1864, a score of young men drifted into St. Albans, a little Vermont town just south of the Canadian border. They arrived in small groups by train and coach, took rooms in local hotels, and began to pass time around town, observing the daily routines of the citizens.
On October 19, they simultaneously held up three local banks. There they revealed themselves to be Confederate soldiers, and as they collected the money they required the bank officers to take an oath of fealty to the South. Then they made off across the border. “They must have either had a guide who was acquainted with the road or had made a personal examination,” wrote one investigator, “because there were places in the road where strangers would have gone the wrong way, but they made no mistake.”
In all, the raiders made off with $208,000, about $3.2 million in today’s dollars. They were apprehended, but the Canadian authorities refused to extradite them, and their leader, Bennett Young, traveled in Europe until it was safe to return to Kentucky after the war. His exploit became the northernmost land action in the Civil War.
Choose a prime number p, draw a p×p array, and fill it with integers like so:
Now: Can we always find p cells that contain prime numbers such that no two occupy the same row or column? (This is somewhat like arranging rooks on a chessboard so that every rank and file is occupied but no rook attacks another.)
The example above shows one solution for p=11. Does a solution exist for every prime number? No one knows.
Patented in 1992 by Celess Antoine. Some things don’t need a lot of explaining.
If you live in an arid climate there’s an alternate solution.
Erik Satie’s 1893 composition Vexations bears an inscrutable inscription: “In order to play the theme 840 times in succession, it would be advisable to prepare oneself beforehand, and in the deepest silence, by serious immobilities.” This seems to mean that the piece should be repeated 840 times in performance, which would take 12-24 hours, depending on how you interpret the tempo marking “Très lent.”
“It is perhaps not surprising that few of the performances [Gavin] Bryars lists have been complete,” writes Robert Orledge in Satie the Composer, “for with the bass theme repeated between each 13-beat harmonization, it recurs 3,360 times.”
“It is probable that Satie’s vexations are those expressed in the latter part of his difficult relationship with Suzanne Valadon, that is to say, somewhere between April and early June 1893.”
A puzzle by Angelo Lewis, writing as “Professor Hoffman” in 1893:
A man went into a shop in New York and purchased goods to the amount of 34 cents. When he came to pay, he found that he had only a dollar, a three-cent piece, and a two-cent piece. The tradesman had only a half- and a quarter-dollar. A third man, who chanced to be in the shop, was asked if he could assist, but he proved to have only two dimes, a five-cent piece, a two-cent piece, and a one-cent piece. With this assistance, however, the shopkeeper managed to give change. How did he do it?