# De Gua’s Theorem

French mathematician Jean Paul de Gua de Malves discovered this three-dimensional analogue of the Pythagorean theorem in the 18th century.

If a tetrahedron has a right-angled corner (such as the corner of a cube), then the square of the area of the face opposite that corner is the sum of the squares of the areas of the other three faces.

Above,

$A_{ABC}^{2} = A_{ABO}^{2} + A_{ACO}^{2} + A_{BCO}^{2}$

# Short-Timer

The shortest jail sentence ever served in Washington state is one minute. From the Seattle Daily Times, Jan. 20, 1906:

[Joe] Munch is a soldier, on leave of absence. On the thirteenth day of August he found garrison life dull and proceeded to get drunk. A policeman found him in this condition and he was hustled off to the police station. In Judge Gordon’s court he was sentenced to thirty days for being drunk and disorderly, but his case was taken to the higher court.

Judge Frater decided that while the soldier’s crime was not enough to merit punishment, for the looks of things he ought to be sent to jail, and have a lesson taught him. Consequently Munch was sentenced to an imprisonment of one minute, something which the clerk who makes out the sentence documents never heard of before and which caused much merriment in court house circles.

“Those who heard the decision were inclined to take it as a joke of the judge’s, until Munch was hustled off to jail and kept there until the second hand of the jailer’s watch had completed the circle of sixty seconds. Munch was so surprised that he hardly knew what was going on and when released decided that the best thing for him to do was to get away for fear the sight of him should cause the judge to inflict a heavier penalty.”

(From the Washington State Library blog.)

“It is a curious thing that every creed promises a paradise which will be absolutely uninhabitable for anyone of civilized taste.” — Evelyn Waugh

“I have read descriptions of Paradise that would make any sensible person stop wanting to go there.” — Montesquieu

“In heaven, all the interesting people are missing.” — Friedrich Nietzsche

“Of the delights of this world man cares most for sexual intercourse, yet he has left it out of his heaven.” — Mark Twain

“I should have no use for a paradise in which I should be deprived of the right to prefer hell.” — Jean Rostand

# Moving Violation

A revealing anecdote from Mank, Richard Meryman’s 1978 biography of Herman J. Mankiewicz, co-writer of Citizen Kane:

Herman was a mischievous child. One day after some misdemeanor, Herman was confined to the house by his mother. To keep him there during her absence, she hid the long stockings he needed for his knickers. Herman went to his mother’s room, put on a pair of her stockings, got on his bike, and rode off to the Wilkes-Barre public library, where he loved to browse among the shelves and to read for hours. When he came out, the precious bike was gone — stolen. Herman’s punishment was permanent. His father never bought him another bike. His mother answered Herman’s pleas by telling him it was all his own fault.

Meryman concludes, “Rosebud, the symbol of Herman’s damaging childhood, was not a sled. It was a bicycle.”

# Words and Numbers

If you write out the numbers from 1 to 5000 in American English (e.g., THREE THOUSAND EIGHT HUNDRED SEVENTY-THREE), it turns out that only one of them has a unique number of characters. Which is it? Spaces and hyphens count as characters.

# Podcast Episode 88: Mrs. Wilkinson and the Lyrebird

Almost nothing was known about Australia’s elusive lyrebird until 1930, when an elderly widow named Edith Wilkinson encountered one on her garden path one February morning. In this week’s episode of the Futility Closet podcast we’ll follow the curious friendship that evolved between Wilkinson and “James,” which led to an explosion of knowledge about his reclusive species.

We’ll also learn how Seattle literally remade itself in the early 20th century and puzzle over why a prolific actress was never paid for her work.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

Sources for our feature on Edith Wilkinson and James:

Ambrose Pratt, The Lore of the Lyrebird, 1933.

Nicolae Sfetcu, The Birds’ World, 2014.

Jackie Kerin, Lyrebird! a True Story, 2012.

“A.P.”, “A Miracle of the Dandenongs,” The Age, Feb. 13, 1932.

Anna Verona Dorris, “The Proud Aristocrat of Birdland,” New Outlook, July-August 1956.

Here’s the full lyrebird video we excerpted on the show:

More lyrebirds mimicking human technology on Futility Closet.

Listener mail:

“The Colorful Front-Gabled Italianate Homes at Damen and 33rd,” Chicago Patterns (accessed Jan. 1, 2016).

John McCarron, “Pilsen Comes Together to Preserve and Build,” LISC Chicago’s New Communities Program, May 3, 2007 (accessed Jan. 1, 2016).

Down to Earth: 9 Stories Above Pilsen (accessed Jan. 1, 2016).

A spite mound.

Wikipedia, “Regrading in Seattle” (accessed Jan. 1, 2016).

Matthew W. Klingle, “Reclaiming Nature: Flattening Hills and Digging Waterways in Seattle,” in Building Nature: Topics in the Environmental History of Seattle and Spokane: A Curriculum Project for Washington Schools, Center for the Study of the Pacific Northwest, University of Washington Department of History (accessed Jan. 1, 2016).

This week’s lateral thinking puzzle is adapted from “Detective Shadow’s” 2000 book Lateral Mindtrap Puzzles. Here’s a corroborating link (don’t click until you’ve listened to the episode).

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

# Progress

Hollinwood, near Manchester, was the scene of a rather novel rat killing match the other day, between Mr. Benson’s fox terrier dog, Turk, and a Mr. Lewis’ monkey, for £5. The conditions of the match were that each one had to kill twelve rats, and the one that finished them the quickest to be declared the winner. You may guess what excitement this would cause in the ‘doggy’ circle. It was agreed that Turk was to finish his twelve rats first, which he did, and in good time, too, many bets being made on the dog after he had finished them. After a few minutes had elapsed it now came the monkey’s turn, and a commotion it caused. Time being called, the monkey was immediately put to his twelve rats, Mr. Lewis, the owner, at the same time putting his hand in his coat pocket and handing the monkey a peculiar hammer. This was a surprise to the onlookers; but the monkey was not long in getting to work with his hammer, and, once at work, he was not long in completing the task set before him. You may talk about a dog being quick at rat killing, but he is really not in it with the monkey and his hammer. Had the monkey been left in the ring much longer you could not have told that his victims had been rats at all — he was for leaving them in all shapes. Suffice it to say the monkey won with ease, having time to spare at the finish. Most persons present (including Mr. Benson, the owner of the dog) thought the monkey would worry the rats in the same manner as the dog does; but the conditions said to kill, and the monkey killed with a vengeance, and won the £5, beside a lot of bets for his owner.

Illustrated Police News, Sept. 4, 1880

# Footwork

The first passenger railway in Australia was powered by convicts. Four-passenger carts ran on hardwood rails from the dock at the head of Norfolk Bay to the main settlement at Port Arthur, some 4.5 miles away. (Click the image to enlarge it.) On steep downhill slopes the carts could reach 30 mph, as observed by Col. Godfrey Mundy on an 1851 visit:

The prisoners seized certain bars crossing the front and back of the carriages, and after pushing them with great toil up a considerable plane, reached the top of a long descent, when, getting up their steam, down they rattled at tremendous speed — tremendous, at least, to lady-like nerves — the chains around their ankles chinking and clanking as they trotted along. … [T]he runners jumped upon the side of the trucks in rather unpleasant proximity with the passengers, and away we all went, bondsmen and freemen, jolting and swaying … a man sitting behind contrived, more or less, to lock a wheel with a wood crowbar when the descent became so rapid as to call for remonstrance.

He added, “Our poor beasts of burthen at the end of the traject seemed terribly jaded, running down with sweat, and saw one of them continually trying to shift his irons from a galled spot on his ankle.” On the return journey that afternoon, the leader asked whether they might stop briefly, as the men had had nothing to eat for 12 hours.

After visiting a similar railway at Ralph Bay Neck in 1847, Lt.-Gov. Sir William Denison wrote, “I must say that my feelings at seeing myself seated, and pushed along by these miserable convicts, were not very pleasant. It was painful to see them in the condition of slaves, which, in fact, they are, waiting for me up to their knees in water.”

(From Robert Hughes, The Fatal Shore, 1987.)

# “The Peace Problem”

In 1984, at the height of the Cold War, Ukrainian chess journalist F.S. Bondarenko dedicated this puzzle to English chess editor A.J. Roycroft in the spirit of peace and goodwill.

White’s army is arranged as above. Add Black’s army (the standard complement of 8 pieces and 8 pawns) so that no piece of either color is under attack.

# Unquote

“Congress is so strange. A man gets up to speak and says nothing. Nobody listens — and then everybody disagrees.” — Russian actor Boris Marshalov, after visiting the House of Representatives