Michigan art teacher Ray Villafane found enough success as a clay and wax sculptor to quit his job in 2006, but his career really took off when he changed media — the Wall Street Journal now calls him “the Picasso of pumpkin carving.”
(Thanks, Bill.)
Future poet laureate John Betjeman wrote this at age 13 as a “prep” exercise:
Whatever will rhyme with Summer?
There only is “plumber” and “drummer”:
Why! the cleverest bard
Would find it quite hard
To connect with the Summer — a plumber!
My Mind’s getting glummer and glummer
Hooray! there’s a word besides drummer;
Oh, I will think of some
Ere the prep’s end has come
But the rhymes will get rummer and rummer.
Ah! If the bee hums, it’s a hummer;
And the bee showeth signs of the Summer;
Also holiday babels
Make th’porter gum labels,
And whenever he gums, he’s a gummer!
The cuckoo’s a goer and comer
He goes in the hot days of Summer;
But he cucks ev’ry day
Till you plead and you pray
That his voice will get dumber and dumber!
The Soviet Tupolev Tu-4 strategic bomber of the 1950s was a reverse-engineered copy of the American Boeing B-29 Superfortress. Stalin wanted a strategic bomber, so when three B-29s were forced to land in Soviet territory in 1944, he ordered clones made, and 20 were ready by 1947, despite the engineering challenges caused by non-metric American specifications.
The Soviets revealed their coup during a Moscow parade in August 1947. When three aircraft flew overhead, Western analysts assumed they were the three captured B-29s. Then a fourth appeared.
(Thanks, Kevin.)
In 1897, shortly after Zona Shue was found dead in her West Virginia home, her mother went to the county prosecutor with a bizarre story. She said that her daughter had been murdered — and that her ghost had revealed the killer’s identity. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Greenbrier Ghost, one of the strangest courtroom dramas of the 19th century.
We’ll also consider whether cats are controlling us and puzzle over a delightful oblivion.
The presence of an inconvenient roadway prevented architect Donato Bramante from making Milan’s Santa Maria presso San Satiro as grand as he’d hoped — so he painted a fictional apse in a shallow niche that’s only a few feet deep.
Created in 1477, it’s one of the earliest examples of trompe l’oeil in the history of art.
You have 12 coins that appear identical. Eleven have the same weight, but one is either heavier or lighter than the others. How can you identify it, and determine whether it’s heavy or light, in just three weighings in a balance scale?
This is a classic puzzle, but in 1992 Washington State University mathematician Calvin T. Long found a solution “that appears little short of magic.” Number the coins 1 to 12 and make three weighings:
First weighing: 1 3 5 7 vs. 2 4 6 8
Second weighing: 1 6 8 11 vs. 2 7 9 10
Third weighing: 2 3 8 12 vs. 5 6 9 11
To solve the problem, note the result of each weighing and assemble a three-digit numeral in base 3 as follows:
Left pan sinks: 2
Right pan sinks: 0
Balance: 1
For example, if coin 7 is light, that produces the number 021 in base 3. Now converting that to base 10 gives 7, the number of the odd coin, and an examination of the weighings shows that it must be light. Another example: If coin 2 is heavy, then we get 002 in base 3, which is 2 in base 10. Note that it’s possible to get an answer that’s higher than 12, e.g. when coin 7 is heavy — in that case subtract the base-10 answer you get from 26.
Another curious method to solve the classic puzzle, this one involving verbal mnemonics, appeared in Eureka in 1950.
(Calvin T. Long, “Magic in Base 3,” Mathematical Gazette 76:477 [November 1992], 371-376.)
09/30/2018 UPDATE: Due to an error in the original paper, the weighings I originally specified don’t work in every case — in the third weighing, the left pan should contain 2 3 8 12, not 1 2 8 12. I’ve amended this in the post above; everything should work now. Sorry for the error; thanks to everyone who wrote in.
I saw a woman sleeping. In her sleep she dreamt Life stood before her, and held in each hand a gift — in the one Love, in the other Freedom. And she said to the woman, ‘Choose!’
And the woman waited long: and she said: ‘Freedom!’
And Life said, ‘Thou hast well chosen. If thou hadst said, ‘Love,’ I would have given thee that thou didst ask for; and I would have gone from thee, and returned to thee no more. Now, the day will come when I shall return. In that day I shall bear both gifts in one hand.’
I heard the woman laugh in her sleep.
— Olive Schreiner, Dreams, 1891
A neat observation by Japanese mathematician Jun Maekawa: If an origami model can be flattened without damage, then at any vertex (meeting of edges) in its crease pattern the number of “valley” folds and “mountain” folds always differ by two.
The single-vertex crease pattern above has five mountain folds (folds whose outer surface is colored) and three valley folds (folds whose inner surface is colored). (The fifth mountain fold is a bit hard to notice in this example — it’s folded flat at bottom right.)
One consequence of this is that every vertex has an even number of creases, and therefore that the regions between the creases can be colored with two colors.
Paper folder Toshikazu Kawasaki found a related theorem: At any vertex, the sum of all the odd angles is 180 degrees (and likewise the even).
It was at the place afterwards called Solenhofen. The weather was miserable, as Jurassic weather usually was. The rain beat steadily down, and carbon dioxide was still upon the earth.
The Archaeopteryx was feeling pretty gloomy, for at that morning’s meeting of the Amalgamated Association of Enaliosaurians he had been blackballed. He was looked down upon by the Pterodactyl and the Ichthyosaurus deigned not to notice him. Cast out by the Reptilia, and Aves not being thought of, he became a wanderer upon the face of the earth. ‘Alas!’ sighed the poor Archaeopteryx, ‘this world is no place for me.’ And he laid him down and died; and became imbedded in the rock.
And ages afterward a featherless biped, called man, dug him up, and marvelled at him, crying, ‘Lo, the original Avis and fountain-head of all our feathered flocks!’ And they placed him with great reverence in a case, and his name became a by-word in the land. But the Archaeopteryx knew it not. And the descendant for whom he had suffered and died strutted proudly about the barn-yard, crowing lustily cock-a-doodle-do!
— Samuel P. Carrick Jr., in The Fly Leaf, January 1896
From Lee Sallows:
(Thanks, Lee!)
