If you erect equilateral triangles on two adjacent sides of a square and then connect the triangle vertices distant from the square to the square vertex distant from the triangles, you get a third equilateral triangle.
Pleasingly, this works whether the triangles are erected inside or outside the square. It was discovered by French mathematician Victor Thébault.
In 1949 English physician Zachary Cope published The Diagnosis of the Acute Abdomen in Rhyme:
The muscles of the bowel-wall are strong
And by their strength they force the food along;
In rhythmic waves contractions come and go
Making the intestinal contents flow;
So if through any kind of morbid state
A bit of bowell wall invaginate
The muscle-wall may force it on and on
Until far down the lumen it has gone.
The gut below Dilates for its reception
And thus you get what’s called intussusception.
He dedicated the 100-page work to his students. The preface to the fifth edition reads:
I thank those readers who oft write to me
Suggesting things with which I oft agree
But most of all I thank the youth who said
‘I always keep a copy by me bed.’
In Lloyd C. Douglas’ 1929 novel Magnificent Obsession, a doctor dies of a heart attack, leaving behind a journal written in cipher. The first page is shown here. Can you read it?
“Philosophy is the art of asking questions that come naturally to children using methods that come naturally to lawyers.” — David Hills
In 1915, Abel Kiansten and John Nelson patented an alarming precursor to the roller coaster in which a victim on roller skates zooms down a ramp and through a loop-the-loop. This is made safe, the inventors assure us, because the skate wheels are secured to the track and the rider is given a little handle to cling to. “Such a support is necessary because the various positions assumed by the performer during his trip would invariably throw the most active athlete from his upright position if some means were not offered him to remain in a standing position.”
It’s not known whether it was ever built. “Many patents were sound and far-reaching, but as many ideas were simply treacherous,” writes Robert Cartmell in The Incredible Scream Machine, his 1987 history of the roller coaster. “It is a blessing some never left the drawing boards or, when built, were closed by lawsuits. Every deviation with tracks was attempted and the eventual safety codes or inspections by insurances companies became beneficial restraints.”
preterlethal
adj. taking place after death
inhume
v. to lay in the grave
janua
n. a door
The principal trap in almost all theatres is known as the grave trap. This is one of the conventionalisms of the English stage, and is a testimony also the enduring influence of Shakespeare. It is well understood that at some time or another the play of ‘Hamlet’ will be performed in every theatre, and Ophelia‘s grave must therefore be dug in every stage — hence the grave trap. It may be that it is not always placed in the right position to suit the ideas of each new representative of the Royal Dane, and it has happened that it has been found too short for the reception of poor Ophelia‘s coffin; but it is never omitted in the construction of a stage.
— Folger Shakespeare Library Scrapbook, quoted in Paul Menzer, Anecdotal Shakespeare, 2015
A popular puzzle asks the solver to punctuate the following:
John where Willie had had had had had had had had had had had full marks.
The common answer is
John, where Willie had had “had,” had had “had had”; “had had” had had full marks.
But in 1955 a contributor to Eureka pointed out that a competing solver might have reversed the two phrases:
John, where Willie had had “had had,” had had “had”; “had had” had had full marks.
And in that case we might observe:
In the punctuation of the above, A, where B had had “… had had ‘had,’ had had ‘had had’; ‘had had’ had had …”, had had “… had had ‘had had,’ had had ‘had’; ‘had had’ had had …”; “had had had had had had had had had had had” had had two possible interpretations.
That observation itself can be punctuated in two different ways — a remark that might be communicated using an even longer string of hads. And so on forever — “there exist intelligible sentences containing (14 × 3n – 3) successive had‘s, where n is any non-negative integer.” “The solution of this recurrence relation is left as an exercise for the student.”
(“By Induction,” Eureka 18 [November 1955], 14. See Over and Out.)
During the Battle of Gettysburg, Battery B of the 1st Rhode Island Light Artillery were loading a Napoleon cannon when a Confederate shell scored a direct hit on the muzzle, killing two men. Corporal James Dye and Sergeant Albert Straight tried to force another round into the tube with a rammer and an ax, but the ball remained lodged in the dented muzzle until a second Confederate shell struck the cannon’s wheel, putting it out of commission. The spiked gun now stands in the Rhode Island statehouse in Providence.
Even more impressive, in the same battle Captain Hubert Dilger, commander of the 1st Ohio’s guns, personally sighted a shot that seemed to have no effect on its target, an enemy cannon. Only when he sighted it through field glasses did he realize what he’d done: “I have spiked a gun for them, plugging it at the muzzle.”
“It would be hard to calculate the odds of such an occurrence happening,” writes Michael Sanders in More Strange Tales of the Civil War. “Just hitting a gun with a ball would be considered a great shot. This would be equivalent to Robin Hood splitting an arrow with another arrow. Captain Dilger could truly say that he could never do that again even if he tried.”
A puzzle from the excellent Riddler feature at FiveThirtyEight, via Oliver Roeder’s 2018 collection The Riddler:
Your eccentric friend Nigel flies from Heathrow to an airport somewhere in the 48 contiguous states, then hires a car and drives around the country, touching the Atlantic and Pacific Oceans and the Gulf of Mexico, then returns to the airport at which he started and flies home. If he crossed the Ohio River once, the Missouri River twice, the Mississippi River three times, and the Continental Divide four times, then there’s one state that we can say for certain that he visited on his trip. What is it?
Korf’s Clock
Korf’s clock is of a novel sort
In which two pairs of hands are used:
One pair points forwards as it ought,
The other backwards a la Proust.
When it says eight it’s also four,
When it says nine it’s also three;
A single glance and you no more
Need fear the ancient Enemy.
For with this wondrous clock you’ll find
As, Janus-like, it turns about
(To such an end it was designed)
Time simply cancels itself out.
Palmström’s Clock
But Palmström’s clock has a “higher” power,
Balanced as lightly as a flower.
Scorning a set pedestrian pace,
It keeps time with a certain grace
And will, in answer to a prayer,
Go en retard, en arriéré.
One hour, two hours, three hours indeed,
Sympathizing with our need!
Though clockwork in its outward part
It hides within — a tender heart.
— Christian Morgenstern
Above: Built in 1586, the town hall in the old Jewish ghetto of Prague bears two clocks: a traditional clock tower with four faces bearing Roman numerals and a second clock bearing Hebrew numerals. The hands on the conventional clocks turn clockwise; those on the Hebrew clock turn counterclockwise. (Thanks, Danesh.)
