If we have two numbers a and b such that ab + 1 is square, then it’s always possible to find a number c for which ac + 1 and bc + 1 are both square. For example, 8 × 3 + 1 = 25 = 52, and 8 × 21 + 1 = 169 = 132 and 3 × 21 + 1 = 64 = 82.
Proof:
If ab + 1 = m2, then set c = a + b + 2m. Now
ac + 1 = a2 + ab + 2am + 1 = a2 + 2am + m2 = (a + m)2
bc + 1 = ab + b2 + 2bm + 1 = b2 + 2bm + m2 = (b + m)2
Via Edward Barbeau, Power Play, 1997.
Every March since 2010, a white stork named Yaren has departed Africa, flown to the village of Eskikaraağaç in Turkey, and landed on the boat of fisherman Adem Yılmaz on the shore of Uluabat Lake. It spends six months in the village, fishing with Yılmaz every morning, then returns to Africa.
A statue of the two now stands in the village’s central square. A live broadcast of stork’s nest is here.
calophantic
adj. pretending or making a show of excellence
velleity
n. a mere wish, unaccompanied by an effort to obtain it
fode
v. to lead on with delusive expectations
magnoperate
v. to magnify the greatness of
Roman diplomat Sidonius Apollinaris describes the hunting skill of Visigoth king Theodoric II:
If the chase is the order of the day, he joins it, but never carries his bow at his side, considering this derogatory to royal state. … He will ask you beforehand what you would like him to transfix; you choose, and he hits. If there is a miss … your vision will mostly be at fault, and not the archer’s skill.
(Quoted in Norman Davies, Vanished Kingdoms, 2012.)
The British post office had to make sense of this address in 1893. It reads “The Right Hon. Sir James Fergusson, P.C., 25, Tedworth Square, S.W.”
Ironically Fergusson had been postmaster-general of Australia.
The writer was Thomas Denman, the future governor-general. The first page of the letter is below: “Dear Sir James, — I hardly think of coming before 11th to London. I am afraid I might …”
Princeton mathematician John Horton Conway memorized π to more than a thousand decimal places by marrying it to the periodic table of the elements:
3 Neutronium 1415926535 Hydrogen 8979323846 Helium 2643383279 Lithium 5028841971 Beryllium …
Between each pair of elements are sandwiched ten digits of π. (Neutronium is Andreas von Antropoff’s notional “element of atomic number zero,” an element with zero protons in its nucleus.) This approach to memorizing digits has a number of virtues:
To remember the elements themselves Conway devised a long mnemonic. It begins
Newt? Hy! He Likes Beryl’s Boring Car for Nites Out in Florid Neon
for
Nn H He Li Be B C N O F Ne.
See the paper below for the whole package — by including unconfirmed hypothetical elements, it encodes 120 mouthfuls, or 1,200 digits.
(John Conway, “Chemical π,” Mathematical Intelligencer 38:4 [December 2016], 7-10.)
Lisbon’s Pavilhão do Conhecimento science museum has four more onlookers than are commonly recognized.
In 2015 Nature published an alarming article suggesting that dragons are real and had only gone to sleep during the Little Ice Age. A medieval document discovered “under a pile of rusty candlesticks” in the Bodleian Library showed that the creatures were once common but had entered a state of brumation when temperatures dropped and their traditional diet of knights began to thin. Rising temperatures in the modern age have correlated with increasing mentions in fictional literature, which “suggests that these fire-breathing lizards are being sighted more frequently.”
It gets worse: “Sluggish action on global warming is set to compound the problem, and policies such as the restoration of knighthoods in Australia are likely to exacerbate the predicament yet further by providing a sustained and delicious food supply.” The date of the article was April 2.
(Andrew J. Hamilton, Robert M. May, and Edward K. Waters, “Here Be Dragons,” Nature 520:7545 [April 2, 2015], 42-43.)
In 1991, artist Michael Dennis installed his sculpture Reclining Figure in Vancouver’s Guelph Park.
In 2012, prankster Viktor Briestensky erected the sign below at the park’s southwest corner.
Park staff initially removed the sign, but when a petition gathered 1,800 signatures they replaced it in 2014. The city now recognizes it as an official public art installation.
“If it were not for the intellectual snobs who pay — in solid cash — the tribute which philistinism owes to culture, the arts would perish with their starving practitioners. Let us thank heaven for hypocrisy.” — Aldous Huxley
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