A puzzle by H.A. Thurston, from the April 1947 issue of Eureka, the journal of recreational mathematics published at Cambridge University:
Bottema’s Theorem
Grab point C above and drag it to a new location. Surprisingly, M, the midpoint of BaAb, doesn’t move.
This works for any triangle — draw squares on two of its sides, note their common vertex, and draw a line that connects the vertices of the respective squares that lie opposite that point. Now changing the location of the common vertex does not change the location of the midpoint of the line.
It was discovered by Dutch mathematician Oene Bottema.
The Aventine Keyhole
The keyhole of the Priory of the Knights of Malta in Rome presents a perfectly framed view of Saint Peter’s Basilica.
It’s not clear whether this is a happy accident or a deliberate design. The property lies in the piazza Cavalieri di Malta, which was designed in 1765 by the supremely imaginative Giovanni Battista Piranesi — who imagined the Aventine Hill as a sacred ship that would sail to the heavens.
Unquote
“Man is certainly crazy. He could not make a mite, and he makes gods by the dozen.” — Montaigne
Podcast Episode 347: The Cottingley Fairies
In 1917, two young cousins carried a camera into an English dell and returned with a photo of fairies. When Arthur Conan Doyle took up the story it became a worldwide sensation. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Cottingley Fairies, a curiosity that would remain unexplained for most of the 20th century.
We’ll also remember a ferocious fire and puzzle over a troublesome gnome.
The Friendship Medals
At the 1936 Olympics, Japanese pole vaulters Sueo Oe and Shuhei Nishida tied for second place, and the Japanese team were told to decide who should claim second place and who third.
After a long discussion, the team chose to favor Nishida, who had cleared 4.25 meters at his first attempt.
When they returned to Japan, Nishida and Oe had a jeweler cut each medal in half and then join the disparate halves, so that each man had a new medal, half silver and half bronze.
“The Horse of Joy”
The September 1918 issue of Popular Science Monthly describes an amusement introduced at Coney Island by Minnesota inventor Otto Fritsche: a horse made of double-walled aluminum. The patron wears a pair of shoulder straps and a gasoline engine drives the thing forward.
Aside from the fact that the contraption is supported in the rear by a pair of large wheels, that the front is supported by a human being, that a periscope protrudes from the head, and that exhaust gases puff from its ears, Otto believes it will be mistaken for a real animal.
“We would like to interview any man who has tried this form of amusement and has survived.”
Round Here
New Zealand’s Egmont National Park is pleasingly circular. Created in 1881, the reserve was specified to cover a 6-mile radius surveyed from the summit of Mount Taranaki, one of the most symmetrical volcanic cones in the world. The result is an almost perfect circle of 33,500 hectares — and it’s surrounded by pasture, which makes the boundary visually distinct.
In a Word
thalassic
adj. of or relating to seas and oceans
dégringolade
n. a quick deterioration or breakdown, as of a situation or circumstance
supersalient
adj. leaping upon
sperate
adj. hoped for; not hopeless
Shipwreck With a Surviving Dog, by the Danish artist Carl Bille (1815–1898).
“A Quaint Address”
Recently I came across a letter sent to me some years ago by a cousin and addressed in the curious manner here shown. The tune is taken from part of an old round called ‘Big Ben.’ In spite of the quaint address the letter was promptly delivered. — Mrs. Andrew Wall, Edinburgh
— Strand, February 1911