In August 1883 James Wallis, the chief of police on the small island of Rodrigues in the western Indian Ocean, added this note to his official report for the month:
On Sunday the 26th the weather was stormy, with heavy rain and squalls; the wind was from SE, blowing with a force of 7 to 10, Beaufort scale. Several times during the night (26th-27th) reports were heard coming from the eastward, like the distant roar of heavy guns. These reports continued at intervals of between three and four hours, until 3 pm on the 27th, and the last two were heard in the direction of Oyster Bay and Port Mathurie.
It wasn’t gunfire. It was the “death cry” of Krakatoa, 3,000 miles away in Indonesia — the loudest sound in recorded history.
If three circles “kiss,” like the black circles above, then a fourth circle can be drawn that’s tangent to all three. In 1643 René Descartes showed that if the curvature or “bend” of a circle is defined as k = 1/r, then the radius of the fourth circle can be found by
The ± sign reflects the fact that two solutions are generally possible — the plus sign corresponds to the smaller red circle, the minus sign to the larger (circumscribing) one.
Frederick Soddy summed this up in a poem in Nature (June 20, 1936):
The Kiss Precise
For pairs of lips to kiss maybe
Involves no trigonometry.
‘Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.
Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance from the center.
Though their intrigue left Euclid dumb
There’s now no need for rule of thumb.
Since zero bend’s a dead straight line
And concave bends have minus sign,
The sum of the squares of all four bends
Is half the square of their sum.
To spy out spherical affairs
An oscular surveyor
Might find the task laborious,
The sphere is much the gayer,
And now besides the pair of pairs
A fifth sphere in the kissing shares.
Yet, signs and zero as before,
For each to kiss the other four
The square of the sum of all five bends
Is thrice the sum of their squares.
Horses are difficult to manage onstage, so in 1901 music hall performer Alexander Braatz invented this ingenious alternative. The actor’s own legs masquerade as those of his horse, and a system of levers and cords moves the hind legs as well.
False human legs are attached at each side to give the appearance that the performer is mounted; his real feet “are advantageously covered by large clumsy hoof-like coverings.” I suppose you could even race these things between rehearsals.
A gentleman, who had been described as a ‘Pettifogger,’ accused another gentleman, whom he had styled a ‘Fish-fag,’ with an assault. It being a very intricate point, it was of course referred to the Lord Mayor. It stood as follows: — ‘Whether puffing a cloud of tobacco-smoke in a man’s face constituted an assault?’ After some grave consultation with that encyclopaedia of wisdom, Mr. Hobler, the decision ran thus — The Lord Mayor: ‘There has been no assault; nothing but words, words.’ — Complainant: ‘I beg pardon, my Lord.’ — The Lord Mayor: ‘Well, then, all smoke, if you please, or words and puffs. There have been no blows.’ — Now we beg his Lordship’s pardon. Pray what is a puff but a blow?
Consider them in turn. A can’t be true because some of the other statements contradict one another (for example, C and D). B can’t be true because it implies that C is also true. Since A and B are false, C is also false, and likewise D. But E is true, and this makes F false. So the answer is E.
From Crux Mathematicorum, 1979, 83, Problem 357, via Ross Honsberger’s More Mathematical Morsels, 1991.
Stewardess Violet Jessop was both cursed and blessed — during the 1910s she met disaster on all three of the White Star Line’s Olympic class of gigantic ocean liners, but she managed to escape each time.
In this episode of the Futility Closet podcast we’ll accompany Violet on her three ill-fated voyages, including the famous sinkings of the Titanic and the Britannic, and learn the importance of toothbrushes in ocean disasters.
We’ll also play with the International Date Line and puzzle over the identity of Salvador Dalí’s brother.
