Retired Pittsburgh math teacher Walter W. Horner devised this doubly magic square in 1955:
Each row, column, and long diagonal produces both a sum of 840 and a product of 2058068231856000.
And Rodolfo Marcelo Kurchan of Buenos Aires discovered this remarkable square in 1991:
Each number contains all 10 digits — and so does the magic sum, 4129607358.
In 1998, California physician Donald L. Unger wrote to the editors of Arthritis & Rheumatism to report a “50-year controlled study by one participant.” His mother had told him that cracking his knuckles would lead to arthritis, so for 50 years the science-minded Unger had cracked the knuckles of his left hand at least twice a day, more than 36,500 times in all, and left the right uncracked as a control. After 50 years he found no arthritis in either hand and no differences between the two hands.
“This result calls into question whether other parental beliefs, e.g., the importance of eating spinach, are also flawed,” Unger wrote. “Further investigation is likely warranted.”
The editors invited a response from Robert L. Swezey, who had published an earlier investigation in the Western Journal of Medicine. Swezey said that his own study had been inspired when his 12-year-old son’s grandmother had warned him that cracking his knuckles would cause arthritis. “It is now 22 years later and he continues to enjoy frequent KC without manifestations or evidence of arthritis.”
With motherly advice thrown into doubt, Swezey wondered whether knuckle cracking might even prevent osteoarthritis. “The possible utilization of KC by managed care providers as an economic, noninvasive, home preventative treatment for arthritis of the hands should be given further consideration,” he concluded. “A clear distinction between hand wringing related to managed care procedures and therapeutic KC will have to be made.”
(Does knuckle cracking lead to arthritis of the fingers? Unger DL. Arthritis Rheum. 1998 May;41(5):949-50.) (Thanks, Bob.)
The first recorded performance of Hamlet took place at sea, aboard the East India ship Red Dragon off the coast of Africa in 1607. Capt. William Keeling’s diary entry for Sept. 5 reads: “I sent the interpreter according to his desier abord the Hector whear he brooke fast and after came abord me wher we gave the tragedie of Hamlett.”
It’s impossible to trisect an angle using a compass and a straightedge, but in 1947 Leo Moser showed how to do it with a pocketwatch. At noon align the watch’s hands with one side of the angle (above, XII), then wait until the minute hand has crossed to the other side (III). At that point the hour hand will have measured one-twelfth of the angle. Double that twice and you have your trisection.
“Now you can trisect an angle anytime, anyplace, for anyone who asks,” writes Underwood Dudley in A Budget of Trisections. “But no one ever will.”
Does every closed curve contain the vertices of a square?
No one knows.
If God exists outside space and time, then how can he be omnipresent, present in all places at all times? If he exists within it, how could he have created it? How could a creation (or anything) take place outside time?
2015 = 4 + 8 + 4 + 9 + 3 + 3 + 1 + 9 + 6 + 7 + 7 + 7 + 1 + 1 + 4 + 0 + 7 + 4 + 1 + 4 + 3 + 9 + 5 + 8 + 6 + 0 + 1 + 2 + 9 + 6 + 0 + 4 + 7 + 1 + 9 + 1 + 3 + 0 + 3 + 2 + 3 + 8 + 8 + 8 + 8 + 3 + 2 + 8 + 4 + 9 + 3 + 7 + 8 + 8 + 8 + 9 + 3 + 4 + 1 + 7 + 1 + 2 + 4 + 6 + 3 + 6 + 4 + 6 + 1 + 2 + 8 + 2 + 5 + 3 + 5 + 5 + 3 + 5 + 1 + 9 + 7 + 0 + 3 + 0 + 8 + 1 + 3 + 9 + 9 + 2 + 8 + 9 + 5 + 7 + 8 + 3 + 3 + 0 + 8 + 5 + 9 + 5 + 6 + 8 + 3 + 2 + 6 + 3 + 1 + 8 + 8 + 3 + 5 + 1 + 0 + 9 + 0 + 1 + 9 + 6 + 3 + 2 + 2 + 5 + 1 + 3 + 8 + 3 + 9 + 4 + 4 + 5 + 9 + 5 + 9 + 2 + 7 + 1 + 1 + 5 + 7 + 6 + 4 + 9 + 5 + 1 + 8 + 0 + 4 + 1 + 5 + 4 + 0 + 1 + 8 + 3 + 1 + 4 + 6 + 5 + 9 + 6 + 1 + 7 + 1 + 1 + 0 + 2 + 0 + 2 + 2 + 8 + 3 + 0 + 0 + 8 + 9 + 6 + 5 + 0 + 2 + 9 + 2 + 1 + 7 + 7 + 5 + 8 + 7 + 7 + 9 + 7 + 2 + 9 + 0 + 1 + 8 + 8 + 6 + 9 + 1 + 2 + 8 + 2 + 7 + 7 + 5 + 4 + 3 + 6 + 0 + 9 + 5 + 4 + 1 + 0 + 1 + 0 + 0 + 3 + 8 + 4 + 0 + 4 + 2 + 1 + 8 + 1 + 2 + 8 + 9 + 4 + 6 + 0 + 8 + 3 + 7 + 6 + 3 + 8 + 8 + 8 + 5 + 5 + 9 + 2 + 4 + 7 + 7 + 5 + 3 + 0 + 7 + 4 + 6 + 1 + 6 + 8 + 6 + 4 + 3 + 7 + 0 + 2 + 5 + 8 + 1 + 3 + 7 + 9 + 8 + 7 + 3 + 3 + 6 + 3 + 4 + 7 + 5 + 8 + 8 + 5 + 2 + 6 + 5 + 6 + 6 + 6 + 6 + 0 + 8 + 6 + 0 + 6 + 6 + 9 + 0 + 8 + 2 + 5 + 6 + 1 + 1 + 3 + 2 + 6 + 9 + 6 + 0 + 9 + 4 + 5 + 2 + 4 + 2 + 5 + 1 + 2 + 5 + 7 + 6 + 8 + 8 + 0 + 6 + 9 + 9 + 8 + 7 + 1 + 3 + 4 + 0 + 9 + 4 + 6 + 1 + 5 + 0 + 8 + 4 + 3 + 6 + 8 + 3 + 1 + 5 + 2 + 3 + 4 + 0 + 1 + 0 + 3 + 5 + 3 + 4 + 1 + 8 + 1 + 0 + 3 + 2 + 6 + 6 + 3 + 0 + 1 + 4 + 1 + 9 + 3 + 7 + 7 + 6 + 8 + 2 + 0 + 6 + 8 + 2 + 7 + 2 + 3 + 6 + 4 + 4 + 3 + 4 + 2 + 2 + 2 + 3 + 9 + 8 + 5 + 3 + 6 + 2 + 0 + 2 + 1 + 6 + 5 + 9 + 5 + 6 + 6 + 3 + 0 + 8 + 0 + 7 + 2 + 4 + 7 + 5 + 4 + 0 + 4 + 6 + 0 + 0 + 2 + 5 + 4 + 4 + 7 + 8 + 2 + 8 + 2 + 2 + 9 + 5 + 1 + 6 + 7 + 4 + 4 + 6 + 1 + 3 + 6 + 4 + 7 + 4 + 6 + 0 + 9 + 3 + 7 + 5
2015137 = 484933196777114074143958601296047191303238888328493788893417124636461282
535535197030813992895783308595683263188351090196322513839445959271157649518041540
183146596171102022830089650292177587797290188691282775436095410100384042181289460
837638885592477530746168643702581379873363475885265666608606690825611326960945242
512576880699871340946150843683152340103534181032663014193776820682723644342223985
362021659566308072475404600254478282295167446136474609375
(Thanks, Pablo.)
Fritz Zwicky referred to his colleagues at the Mount Wilson Observatory as “spherical bastards” because they were bastards whichever way one looked at them.
anserine
adj. of or resembling a goose
In 1936, Polish mathematician Stanislaw Mazur offered a live goose to the first person who could determine whether every Banach space has a Schauder basis. Thirty-seven years later, his Swedish colleague Per Enflo claimed the prize. The ceremony was broadcast throughout Poland. (Thanks, Jeremy.)
In the public gardens at Halifax, there is an eccentric goose that seems to manifest a genuine affection. Whenever a certain old gentleman, whose name we do not know, approaches the pond and calls ‘Bobby,’ the goose will leave the pond and sit beside him, and when he leaves to go home, will follow close at his feet, like a dog, to the gate, and sometimes into the street, when it has to be forcibly put back, to its manifest disgust, for it goes off to its native element twisting its tail with indignation, and giving vent to sundry discordant squeaks. The old gentleman says he has never fed it, or petted it in any way, which makes it more remarkable; but we are told by a frequenter of the gardens that about two or three years ago a man used to come there and feed this identical goose regularly, so we are inclined to think that it is a case of mistaken identity on the part of his gooseship. Anyway, it is an interesting question for ornithologists to solve, whether geese (supposed to be the most stupid of birds) have memory and can experience the sensation of gratitude.
— James Baird McClure, ed., Entertaining Anecdotes From Every Available Source, 1879