Can every convex polyhedron be “unfolded” into a shape that doesn’t overlap itself, like this dodecahedron?
Surprisingly, no one knows.
The Renaissance artist Albrecht Dürer first wondered about this in the early 1500s, and in the ensuing five centuries no one has found a polyhedron that won’t permit it. But one may yet exist.
A problem from Sam Loyd’s Cyclopedia of Puzzles, 1914:
Here is the puzzle of Tom the Piper’s Son, who, as told by ‘Mother Goose,’ stole the pig and away he run. It is known that Tom entered the far gate shown at the top on the right hand. The pig was rooting at the base of the tree 250 yards distant, and Tom captured it by always running directly towards it, while the pig made a bee-line towards the lower corner as shown. Now, assuming that Tom ran one-third faster than the pig, how far did the pig run before he was caught?
Intriguingly, Loyd adds, “The puzzle is a remarkable one on account of its apparent simplicity and yet the ordinary manner of handling problems of this character is so complicated that solvers are asked merely to submit approximately correct answers, based upon judgment and common sense, just to see who can make the best guess. The simple rule for solving it, however, which will doubtless be quite new to our puzzlists, is based upon elementary arithmetic.” What’s the answer?
Arborsculptor Richard Reames created this living bench by training red alders into a congenial shape.
His monograph on tree trunk topiary is called How to Grow a Chair.
See A Natural Seat.
An odd encounter between Thomas Edison and Henry Ford at a Democratic fundraising luncheon at New York’s Biltmore Hotel, 1916, from the memoir of Navy Secretary Josephus Daniels:
I do not suppose anything so strange ever occurred at a luncheon in New York and elsewhere. … After the first course, Edison, pointing to a large chandelier, with many globes, in the middle of the room, said, ‘Henry, I’ll bet anything you want that I can kick the globe off that chandelier.’ It hung high toward the ceiling. Ford said he would take the bet. Edison rose, pushed the table to one side of the room, took his stand in the center and with his eye fixed on the globe, made the highest kick I have ever seen a man make and smashed the globe into smithereens. He then said, ‘Henry, let’s see what you can do.’ The automobile manufacturer took careful aim, but his foot missed the chandelier by a fraction of an inch. Edison had won and for the balance of the meal or until the ice-cream was served, he was crowing over Ford, ‘You are a younger man than I am, but I can out-kick you.’ He seemed prouder of that high kick than if he had invented a means of ending the U-boat warfare.
(Via Edmund Morris’ 2019 biography Edison.) (Thanks, Aditya.)
Consider for example the proceedings that we call ‘games.’ I mean board-games, card-games, ball-games, Olympic games, and so on. What is common to them all? — Don’t say: ‘There must be something common, or they would not be called “games”‘ — but look and see whether there is anything common to all. — For if you look at them you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. To repeat: don’t think, but look! — Look for example at board games, with their multifarious relationships. Board games, what are some? Consider chess, of course, but think also of Monopoly. Now pass to card-games; here you find many correspondences with the first group, but many common features drop out, and others appear. When we pass next to ball-games, much that is common is retained, but much is lost.– Are they all ‘amusing’? Compare chess with noughts and crosses. Or is there always winning and losing, or competition between players? Think of patience. In ball-games there is winning and losing; but when a child throws his ball at the wall and catches it again, this feature has disappeared. Look at the parts played by skill and luck; and at the difference between skill in chess and skill in tennis. Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! And we can go through the many, many other groups of games in the same way; can see how similarities crop up and disappear.
— Wittgenstein, Philosophical Investigations, 1953
In August 1945, a few weeks before the end of World War II, a Soviet delegation presented a replica of the Great Seal of the United States as a gift to American ambassador W. Averell Harriman, who hung it in the study of his Moscow residence.
In 1951, a radio operator at the British embassy overheard American voices on an open radio traffic channel used by the Russian air force. An investigation showed that they’d been beaming radio waves at the ambassador’s office: The gift had contained a passive listening device that could be activated by a radio signal. The Soviets had been listening in on the ambassador’s residence for six years.
When a U-2 spy plane was shot down over Soviet territory in 1960, Henry Cabot Lodge Jr. displayed the device to show that both sides had been guilty of spying.
Glimmering, gone — springtime stream
Lapping … road winding down
The shimmering hill. Hometown
Napping … sweet, solemn dream!
Dream solemn, sweet … napping
Hometown … hill shimmering … the
Down-winding road … lapping
Stream … springtime … gone, glimmering.
Willard R. Espy quotes this in his 1999 book The Best of an Almanac of Words at Play without citing the source. It’s by David L. Stephens.
The fastest man on earth is named Bolt. Is that a coincidence, or did his name influence his choice of career?
In 2015, four curious researchers combed the British medical register looking for practitioners whose surnames seemed apt for their specialties (e.g., a neurologist named Brain). Then they compared the frequency of apt names listed under hospital specialties against their frequency in the register in general. They found that “[t]he frequency of names relevant to medicine and to subspecialties was much greater than that expected by chance.” Some examples:
General surgery: Gore, Butcher, Boyle, Blunt
Urology: Ball, Burns, Cox, Dick, Waterfall
Psychiatry: Downs, Lowe, Bhatti, Moodie, Nutt
Cardiology: Hart, Pump, Payne
Dermatology: Boyle, Hickey
Neurology: Counsell, Panicker
Paediatric medicine: Boys, Gal, Child, Kinder
Also: “Paediatric medicine was much more likely to be Wong than White (10:2), whereas anaesthetists were far more likely to be White than Wong (22:4).” And “One wonders if the comforting words of Dr Lie carry less impact because of the name, or whether consultations with Dr Dark in oncology are made any more ominous.”
(C. Limb et al., “Nominative Determinism in Hospital Medicine,” Bulletin of the Royal College of Surgeons of England 97:1 [2015], 24-26.) (See Doctor Doctor and the Doctor’s Names List.)
In 1915 James Ferguson Smyth invited Hermann Helms to play a practice game at the Manhattan Chess Club. They had reached the position above when Helms, as Black, found a brilliant two-move mate. What is it?
In 1997 a series of eruptions by the nearby Soufrière Hills volcano buried most of Plymouth, Montserrat, making it uninhabitable.
The government was moved to the town of Brades, but nominally Plymouth remains the capital, making it the only ghost town that serves as the capital of a political territory.
