Napoleon’s Theorem

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Image: Wikimedia Commons

Construct equilateral triangles on the sides of any triangle, and their centers will form an equilateral triangle. (This also works if you construct the triangles inward rather than outward. This triangle has the same center as the outward triangle, and the difference in their areas is the area of the original triangle.)

This discovery is traditionally credited to Napoleon, but there’s no evidence supporting that contention. Indeed, this theorem is said to be one of the most frequently rediscovered results in mathematics.

See A Better Nature.

| Science & Math

In a Word

griffonage
n. careless handwriting

Of all editorial writers, Horace Greeley was most noted for illegible copy. On one occasion the ‘modern Franklin’ penned something about ‘Suburban journalism advancing,’ but the typesetter, thinking it one of his famous agricultural articles, launched out wildly with the words, ‘Superb Jerusalem artichokes.’ The stories of the wild work made by compositors with Mr. Greeley’s writing are endless, and probably most of them inventions; but the fiction cannot possibly outdo the reality. One of his editorial headings, ‘William H. Seward,’ was turned into ‘William the Third’; and the quotation from Shakespeare, ”Tis true, ’tis pity, and pity ’tis ’tis true,’ came out ”Tis two, ’tis fifty and fifty, ’tis fifty-two.’ That a sign-painter turned the placard ‘Entrance on Spruce’ to put up on the Nassau Street door during repairs, into ‘Editors on a Spree,’ is probably apocryphal; but the familiar legend that a discharged printer took his note of dismissal and used it for a letter of recommendation, securing a place on the strength of the signature, which was all anybody could read, is likely enough to have been true.

— Travelers’ Record, April 1889

See Pen Mystique.

| Language · Literature

Undisturbed

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Periander ordered two young men to go out by night along a certain road, to kill the first man they met there, and to bury him.

Then he ordered four more men to find those two and kill them. And he sent an even greater number to murder those four.

Periander then set off down the road himself to wait for them.

In this way he ensured that the location of his grave would never be known.

| Death · History

Rational Self-Denial

You are to choose exactly one of two opaque boxes, A and B. A mean demon has put $1,000 in the box he predicted you would not take and nothing in the other. Since you know that the predictions are quite reliable, you can be sure you will pick the wrong box. … [Now suppose] we add a small bonus for taking box B. Some of us are now inclined to say that this modification renders the A option irrational. For it seems that the bonus tips the balance that previously existed between two equally good choices. If taking box A is as rational as taking box B, then the package deal of taking B plus the bonus must be more rational than taking Box A. Yet … if the bonus makes taking B the uniquely rational choice, then you would know that the money was in box A. This knowledge would force you to change your mind in favour of taking box A.

— Roy A. Sorensen, Blindspots, 1988, after Brian Skyrms

Sorensen adds: “Perhaps this reply has some persuasiveness when the bonus is small. But now suppose that the bonus is almost as great as the prize itself, say $900. Wouldn’t it be irrational to forgo a sure $900 by taking box A?”

See Newcomb’s Paradox.

| Science & Math

Contending in Vain

In December 2005, tired of endless credit-card offers, West Hollywood realtor Gary More scrawled NEVER WASTE A TREE across one application and mailed it in.

Chase Visa issued a card to “Never Waste Tree.”

He cut it up.

| Oddities

Crime and Punishment

http://www.google.com/patents/about?id=aY1JAAAAEBAJ

Apparently vexed by bicycle thieves, Adolph Neubauer had a bright idea in 1899: Crank needles up through the seat when the bike isn’t in use “and thus prevent any one from mounting the bicycle without serious injury.”

He got the patent in 1900. Whether it worked is unknown.

| Technology

Red Ink

More notable errors in the New York Times:

  • “A report misidentified the document on which John Hancock put his famous prominent signature. It was the Declaration of Independence, not the Constitution.” (July 14, 1985)
  • “An article about Ivana Trump and her spending habits misstated the number of bras she buys. It is two dozen black, two dozen beige and two dozen white, not two thousand of each.” (Oct. 22, 2000)
  • “A recipe for juniper-flavored gravlax misstated the amount of kosher salt. It is one-half cup, not four cups.” (Nov. 26, 2000)
  • “A report in the ‘Sunday’ pages included erroneous data from the Farmer’s Almanac about occurrences of full moons. The last month with no full moon was February 1980, not February 1866. The next month without a full moon will be February 1999, not some month 2.5 million years from now.” (Feb. 25, 1996)
  • “An article misstated the title of the 1955 film that made James Dean a star. It is ‘Rebel Without a Cause,’ not ‘Rebel With a Cause.'” (May 8, 2000)

See also Erratum.

| Oddities

Fast Friends

England and Portugal have been allies for 600 years:

It is cordially agreed that if, in time to come, one of the kings or his heir shall need the support of the other, or his help, and in order to get such assistance applies to his ally in lawful manner, the ally shall be bound to give aid and succour to the other, so far as he is able (without any deceit, fraud, or pretence) to the extent required by the danger to his ally’s realms, lands, domains, and subjects; and he shall be firmly bound by these present alliances to do this.

That agreement was signed in 1386. It’s the oldest surviving alliance in the world.

| History

Embarrassing Duels

In June 1836, congressmen Daniel Jenifer of Maryland and Jesse A. Bynum of North Carolina met on the dueling ground in Bladensburg, Md. Jenifer had denounced Andrew Jackson’s party and refused to retract his statement. The two men stood 10 feet apart, both fired six times, and, amazingly, both missed six times. They called it a draw.

In The Field of Honor, his 1883 history of dueling, Benjamin Cummings Truman records a strange contest between Capt. Raoul de Vere and Col. Barbier-Dufai, of Paris. The two agreed to settle a quarrel by entering a coach with daggers in their right hands and with their left arms tied, and fighting while the coach was driven twice around the Place du Carousel. Both died.

Even stranger: A Spaniard and a German both loved the daughter of Maximilian II, but the emperor did not want to risk their lives in a conventional duel. Instead he promised the girl’s hand to whichever man could wrestle his opponent into a bag.

“The two gentlemen expressed their willingness to engage in even so ridiculous a contest for so superior a prize, and fought in the presence of the whole court, the contest lasting more than an hour, the Spaniard finally yielding, having been put fairly into the bag by the German, Baron Eberhard, who took it and its Castilian contents upon his back, and very gallantly laid them at the feet of the young lady, to whom he was married the following day. This is the only duel or tournament of the kind on record.”

See En Garde!

| Society