In 1904, adventure novelist H. Rider Haggard awoke from a dream with the conviction that his daughter’s dog was dying. He dismissed the impression as a nightmare, but the events that followed seemed to give it a grim significance. In this week’s episode of the Futility Closet podcast we’ll describe Haggard’s strange experience, which briefly made headlines around the world.
We’ll also consider Alexa’s expectations and puzzle over a college’s name change.
This pretty proof of the Pythagorean theorem is attributed to Leonardo da Vinci. Draw a right triangle and construct a square on each side, and make a copy of the original triangle and add it to the bottom of the hypotenuse square as shown. Now the shaded hexagon in the first figure can be rotated 90 degrees clockwise around the indicated point to occupy the position shown in the second figure. The orange and green quadrilaterals in the second figure are seen to be congruent to those in the first figure: The three shortest sides of the orange quadrilateral in the second figure correspond to their counterparts in the first, and the angles between them are assembled from the same constituents. The same is true of the green quadrilaterals. In each figure the shaded hexagon contains two instances of the original right triangle; remove these and we can see that the two squares in the first figure equal the large square in the second figure, proving Pythagoras.
10/10/2021 UPDATE: A number of readers point out that only the orange quadrilateral here can properly be said to turn; in the second diagram the green quadrilateral has been reflected as well. (Thanks, Mark and Bill.)
From a letter from Mark Twain to Mabel Larkin Patterson of Chicago, Oct. 2, 1908:
The contents of your letter are very pleasant and very welcome, and I thank you for them, sincerely. If I can find a photograph of my ‘Tammany’ and her kittens, I will enclose it in this. One of them likes to be crammed into a corner-pocket of the billiard table — which he fits as snugly as does a finger in a glove and then he watches the game (and obstructs it) by the hour, and spoils many a shot by putting out his paw and changing the direction of a passing ball. Whenever a ball is in his arms, or so close to him that it cannot be played upon without risk of hurting him, the player is privileged to remove it to any one of 3 spots that chances to be vacant.
At the time his cats were named Apollinaris, Beelzebub, Blatherskite, Buffalo Bill, Sour Mash, Tammany, and Zoroaster — “names given them not in an unfriendly spirit,” he wrote, “but merely to practice the children in large and difficult styles of pronunciation.”
“It was a very happy idea. I mean, for the children.”
In a December 1985 letter to the Mathematical Gazette, Middlesex Polytechnic mathematician Ivor Grattan-Guinness writes that Astronomer Royal George Biddell Airy “would sometimes go around the Observatory, and on finding an empty box, insert a piece of paper saying ‘Empty box’ and thereby falsify its description! This last achievement deserves, in my proposal, the name of ‘Airy’s paradox’.”
Three men play a game, agreeing that in each round the loser will double the money of each of the other two. After three rounds, each man has lost one time, and each man has $24. How much did each have at the start of the game?
Which of the two shaded areas is larger, the central disc or the outer ring?
Surprisingly, they’re equal. Each of the concentric circles has a radius 1 unit larger than the last. So the area of the central disc is π × 32 square units, and the area of the outer ring is π × 52 – π × 42 = π × 32 square units. So the two areas are the same.
A brewery stored its beer in a cellar some distance from the bottling plant. The cellar was cooled by pipes that circulated a saline solution from a central cooling unit. The main pipe that connected this cooling unit and the cellar happened to pass near the cellar of a retailer.
The brewery’s owner eventually discovered that the retailer was using the saline solution to cool his own cellar. He sued the retailer for theft, but the judge ruled, “In accordance with Article 242 of the Criminal Code, theft is the unlawful appropriation of commodities belonging to another party. In the present case no theft has been committed, since the saline solution was not misappropriated; rather, it was returned in its entirety to the brewery’s main pipe.”
The brewery owner appealed the case, arguing, “The issue is not the theft of saline solution but the theft of energy. If the saline solution is used to cool the defendant’s cellar in addition to my own, I have to pay more for electricity to operate the central cooling unit.”
The court of appeals ruled: “The saline solution acquires heat from the retailer’s cellar; therefore, energy belonging to the brewery is not being stolen. On the contrary, the brewery is receiving gratuitous energy from the retailer.”
This story appeared in a German scientific monograph, “Questions of Thermodynamical Analysis,” by P. Grassman. In propounding it in May 1990, Quantum added, “We all agree the judge was wrong, but not everyone can correctly explain his error. Can you?”
Letters to the Sydney Morning Herald during the planning of the Sydney Opera House:
“Faced with the nightmare illustrated in your columns, some 25th century Bluebeard’s lair, its ominous vanes pointed skywards apparently only for the purpose of discharging guided missiles or some latter-day nuclear Evil Eye, words fail.”
— W.H. Peters, Sydney, Jan. 31, 1957
“To me, the winning design suggests some gargantuan monster which may have wandered over the land millions of years ago. It certainly is right out of place beside the dignity of the Harbour Bridge.”
— M. Rathbone, Kensington, Jan. 31, 1957
“This whale of a monument to the clever ugliness of ‘modern’ art will be a constant eyesore. Its over-finished roof with many curved surfaces all covered with white tiles will be a glaring monstrosity. Could not the suffering which it will cause be more equitably distributed by constructing the fins in such a way that they will act as giant megaphones and thus keep residents on the north supplied with the dying screams of melodramatic sopranos?”
— J.R.L. Johnstone Beecroft, Feb. 1, 1957
“With all respects to so-called modern art, I feel that the design is completely unbefitting our foreshores. Perhaps the judges had in mind the installation of a Big Dipper on the peak of the roof to help the opera company balance its budget.”
— Jack Zuber, Kingsgrove, Feb. 1, 1957
In 2003 Danish architect Jørn Utzon received the Pritzker Architecture Prize, architecture’s highest honour. The citation read, “There is no doubt that the Sydney Opera House is his masterpiece. It is one of the great iconic buildings of the 20th century, an image of great beauty that has become known throughout the world — a symbol for not only a city, but a whole country and continent.”
Peculiarly British limericks:
There was a young fellow of Beaulieu,
Who loved a fair maiden most treaulieu.
He said, “Do be mine,”
And she didn’t decline,
So the wedding was solemnized deaulieu.
There was a young maid of Aberystwyth,
Who took corn to the mill to make grystwyth,
The miller, named Jack,
With a pat on her back,
Pressed his own to the lips that she kystwyth.
There was a mechalnwick of Alnwick,
Whose opinions were anti-Germalnwick;
So when war had begun,
He went off with a gun
The proportions of which were Titalnwick.
There was a young lady of Slough,
Who went for a ride on a cough.
The brute pitched her off
When she started to coff;
She ne’er rides on such animals nough. (Langford Reed)
A bald-headed judge called Beauclerk
Fell in love with a maiden seau ferk
Residing at Bicester,
Who said when he kicester,
“I won’t wed a man without herk.”
See This Sceptred Isle and Sound Rhymes.
surbate
v. to make one’s feet sore
