~feeds_feedburner_com | Bookmarks (190)

Alexander Shapovalov suggested an unusual coin-weighing problem for the sixth international Kolmogorov math tournament in 2007: A judge is presented with 80 coins that all look the same, knowing that there are either two or three fake coins among them. All the real coins weigh the same and all the fake coins weigh the same, but the fake coins are lighter than the real...

This rock formation, formed possibly thousands of years ago, spans a chasm on Mount Tai, one of the Five Great Mountains of China. It’s said that anyone who crosses the bridge will live forever.

Until 2022, every tiling of the plane eventually repeated itself. Then amateur mathematician David Smith discovered a remarkable tile that will cover an infinite plane but only in a nonperiodic way. This solves an open problem in mathematics — for years researchers had been seeking an aperiodic monotile, or “einstein,” from the German for “one stone.” Technically Smith’s tile, known as the “hat,” must...

Ulrich von Cranach of Hamburg devised this perpetual motion machine in 1664, offering it to drive pumps in mines. An Archimedean screw raises a succession of iron balls that then descend by a wheel that turns the screw. Robert Fludd had proposed a water mill in 1618 that used essentially the same design. The anonymous variant below dates from the Middle Ages.

Proverbs from around the world: See that you are wise, but also learn to appear ignorant. (Armenian) If men could foresee the future, they would still behave as they do now. (Russian) Many have suffered for talking; none ever suffered for keeping silent. (Italian) To listen to a lie is harder than to tell it. (Turkish) Not your friend but your enemy will tell...

I just stumbled into this — in October 1967, IBM published this problem in Eureka, the journal of the Cambridge University Mathematical Society (page 2): The triplets (whose abilities at walking, cycling, and donkey riding are identical) always leave home together at the last possible minute and arrive at school together on the last stroke of the bell. They used to walk the 4...

Imprisoned at Theresienstadt during World War II, Czech composer Rudolf Karel wrote a five-act opera, Three Hairs of the Wise Old Man, on toilet paper using the medicinal charcoal he’d been prescribed for his dysentery. The illness eventually claimed his life, but a sketch of the opera was preserved by a friendly warden, and the orchestrations were finished by Karel’s pupil Zbynek Vostrák.

These two handcarts have the same mass. Newton tells us that equal forces applied to equal masses impart equal accelerations. So why does the second handcart pick up speed more quickly than the first? (This is a Soviet problem; Н is the Russian abbreviation for newtons.)

manqueller n. a man killer; an executioner In 1014, after a decisive victory over the Bulgarian Empire at the Battle of Kleidion, Byzantine emperor Basil II followed up with a singularly cruel stroke. He ordered that his 14,000 prisoners be divided into groups of 100; that 99 of each group be blinded; and that the hundredth retain one eye so that he could lead...

From 1995 to 1998, the journal Philosophy and Literature ran a bad writing contest to mark “the most stylistically lamentable passages found in scholarly books and articles.” The final year’s winners: First prize: The move from a structuralist account in which capital is understood to structure social relations in relatively homologous ways to a view of hegemony in which power relations are subject to...

From an April Fools’ feature in LIFE, April 4, 1938: The photo appeared in a German paper, which claimed the story was American. “To Germans, actual American goings-on are fantastic enough to be April Fools’ tricks.”

When a goose without feet was hatched in Harvard, Nebraska, in 1987, local inventor Gene Fleming adopted the bird, fitted him with baby-sized shoes, and taught him to walk. In time “Andy” learned to swim and fly as well; he gave inspiration to disabled children and received a lifetime supply of shoes from Nike, but it wasn’t to last — in 1991 he was...

From reader Éric Angelini: During a standard chess game, after Black’s fifth move we notice that three rooks have been captured on the same dark square. Which square is it?

If mercy modifies the demands of justice, then to be merciful is perhaps to be unjust. But manifesting injustice is a vice, not a virtue. This seems to mean that mercy is a vice. A sentencing judge has been hired to enforce the rule of law that society has agreed upon. If he tempers this, even through love or compassion, then arguably he’s departing...

A conference is attended by 1,000 delegates from various countries. It’s known that any three delegates can speak together without help, though one of the three may have to serve as interpreter for the other two. Prove that all the attendees can be accommodated in double rooms so that the two occupants of each room can speak to each other.

The beginnings of Algebra I found far more difficult [than Euclid], perhaps as a result of bad teaching. I was made to learn by heart: ‘The square of the sum of two numbers is equal to the sum of their squares increased by twice their product.’ I had not the vaguest idea what this meant, and when I could not remember the words, my...

In the beginning there was Aristotle, And objects at rest tended to remain at rest, And objects in motion tended to come to rest, And soon everything was at rest, And God saw that it was boring. Then God created Newton, And objects at rest tended to remain at rest, But objects in motion tended to remain in motion, And energy was conserved and...

“Everyone believes in the normal law, the experimenters because they imagine that it is a mathematical theorem, and the mathematicians because they think it is an experimental fact.” — Gabriel Lippmann, in a letter to Henri Poincaré (Thanks, Tom.)

Subtitled “A Novel in Woodcuts,” Lynd Ward’s 1929 parable Gods’ Man unfolds in images, making it an important forebear of the modern graphic novel. A young artist makes his way to the big city, where a masked stranger gives him a magic paintbrush. The adventures that follow remark on the roles of love and commerce in an artist’s life; in the end the stranger...

We instinktivly shrink from eny chaenj in whot iz familyar; and whot kan be mor familyar dhan dhe form ov wurdz dhat we hav seen and riten mor tiemz dhan we kan posibly estimaet? We taek up a book printed in Amerika, and honor and center jar upon us every tiem we kum akros dhem; nae, eeven to see forever in plaes ov for...

The product of the distances from N equally spaced points on a unit circle to a point M that lies on the x axis at distance x from circle origin O and on a line passing through the first point, A0, on the circle equals 1 – xN. Discovered by Roger Cotes (1682-1716). Here’s a proof.

From reader Dave King: A certain young lady of Prinknash Was looking decidedly thinknash. Her diet restriction Had proved an addiction And caused her to swiftly diminknash. A hungry young student of Norwich Went into his larder to forwich. For breakfast he usually Had bacon or muesli But today he would have to have porwich. An ethical diner at Alnwick Was suddenly put in...