In the Stars

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In the December 2024 issue of Recreational Mathematics Magazine, Illinois State University mathematician Sunil Chebolu demonstrates that the digits of π can be generated using the positions of stars.

The probability P(x, y) that two randomly chosen positive integers, x and y, are relatively prime is 6/π2. The stars in the night sky appear to be distributed randomly on the celestial sphere, and this suggests a novel experiment: Use the pairwise angular distances between stars to simulate a large random sample of numbers, then pick random pairs and determine the proportion of relatively prime pairs. Equating that with the theoretical probability above should generate an approximation of π.

In Nature in 1995, University of Aston mathematician Robert Matthews used the positions of 100 stars to compute π to within 0.5% of its correct value (3.12772). By expanding the sample to 1,000 stars, Chebolu got an average estimate of 3.141540567, an error of less than 0.002%.

“The above method can also be viewed as a statistical hypothesis test,” Chebolu notes. “Since the error in the estimate for π obtained using this method is pretty low, one may also argue that it supports the hypothesis that the bright stars are randomly distributed on the celestial sphere.”

(Sunil K. Chebolu, “Baking Star π,” Recreational Mathematics Magazine 11:19 [December 2024], 67-70.)

In a Word

postation
n. the placing of one thing after another

consectaneous
adj. succeeding, following as by consequence

resiliating
adj. that resumes or causes to resume a former shape or position

finifugal
adj. shunning the end of something

Jason Allemann built this infinite LEGO domino ring in 2023. Sixty-four dominoes fall in a continuous loop, with a robot circulating perpetually opposite the cascade to restore the tiles to their standing state.

Building instructions are here.

The Illinois

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Image: Wikimedia Commons

In his 1957 book A Testament, Frank Lloyd Wright described a skyscraper a mile high that he hoped to build in Chicago. Atomic-powered elevators would serve a net rentable area of more than 13 million square feet, with covered parking for 15,000 cars and landing decks for 150 helicopters.

Wright imaged it would be “more permanent than the pyramids,” but the plan was never realized. The 528-story building would have been nearly twice as tall as the Burj Khalifa and four times the height of the Empire State Building.

Last Moments

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In 1937 a Sabena Junkers Ju 52 crashed in Ostend — the plane struck a factory chimney while attempting to land in thick fog. Everyone aboard was killed, including Princess Cecilie, the older sister of Prince Philip, later Duke of Edinburgh.

She had been eight months pregnant, and a newborn infant was discovered in the wreckage. It’s speculated that she had given birth during the flight, and that this had led the pilot to try to land in hazardous conditions.

A Glimpse

In his later years Joseph Conrad became obsessed with the opening scene of an unwritten novel that he planned to set in an Eastern European state. “So vividly used he to describe this scene to me,” wrote his friend Richard Curle, “that at last it was as though I had been a witness to it myself”:

“In the courtyard of a royal palace, brilliantly lighted up as for a festival, soldiers are bivouacked in the snow. And inside the palace a fateful council is taking place and the destiny of the country is being decided.”

“I never learned anything more about this novel — I do not know how far Conrad had himself visualized the plot,” Curle wrote, “but as he pictured that opening scene one could almost feel the tension in the air and one almost seemed to be warming one’s hands with the soldiers around their blazing fire.”

(Richard Curle, The Last Twelve Years of Joseph Conrad, 1928.)

“A Square Poem”

This poem, by Lewis Carroll, can be read line by line in the conventional way, but the same text results when it’s scanned “downward” in columns, reading the first word of each of the six lines, then the second, and so on:

I           often     wondered    when     I         cursed

Often       feared    where       I        would     be --

Wondered    where     she'd       yield    her       love,

When        I         yield,      so       will      she.

I           would     her         will     be        pitied!

Cursed      be        love!       She      pitied    me ...