Famously, in a group of 23 randomly chosen people, the chance is slightly higher than 50 percent that two will share a birthday.

In 2014, James Fletcher considered the birth dates of players in the World Cup, who were conveniently organized into squads of 23 people each. He found that 16 of the 32 squads had at least one shared birthday. If data from 2010 World Cup was included, 31 of 64 squads had shared birthdays, still quite close to 50 percent.

If a group numbers 366 people, the probability of a shared birthday is 100 percent (neglecting leap years). But to reach 99 percent certainty we need only 55 people. “It is almost unbelievable that such a small difference between the probabilities 99% and 100% can lead to such a big difference between the numbers of people,” writes Gabor Szekely in Paradoxes in Probability Theory and Mathematical Statistics (1986). “This paradoxical phenomenon is one of the main reasons why probability theory is so wide-ranging in its application.”

Discovered by Princeton mathematician John Horton Conway: If the sides meeting at each vertex of a triangle are extended by the length of the opposite side, as shown, the six resulting endpoints will lie on a circle — and that circle is concentric with a circle inscribed in the triangle.

Also, pleasingly, Wikipedia has a list of things named after John Horton Conway.

In Mathematics in Fun and in Earnest (2006), Nathan Altshiller-Court describes an ancient method of finger arithmetic to compute the product of two numbers in the range 6-10. Each number is assigned to a finger (on both hands):

6: little finger
7: ring finger
8: middle finger
9: index finger
10: thumb

Now, to multiply 7 by 9, hold your hands before you with the thumbs up and touch the ring finger of one hand to the index finger of the other. These two fingers and all the others physically below them number six and count for 60 toward the final result. Above the joined fingers are three fingers on one hand and one on the other — multiply those two values, add the result (3) to the existing 60, and you get the final answer: 7 × 9 = (6 × 10) + (3 × 1) = 63.

“Besides its arithmetical uses, this clever trick may also serve, with telling effect, to enhance the prestige of an ambitious grandfather in the eyes of a bright fourth-grade grandson,” Altshiller-Court observes. “Competent observers report that it is still resorted to by the Wallachian peasants of southern Rumania.”

The unassuming Japanese perennial Paris japonica may have the largest genome of any living organism.

With 150 billion base pairs, the DNA from a single cell stretched out end to end would cover more than 300 feet.

These compounds are named housane, churchane, basketane, and penguinone.

Below: To celebrate the 2012 London Olympics, chemists Graham Richards and Antony Williams offered a molecule of five rings. They called it olympicene.

In 1971, physicist Joseph C. Hafele and astronomer Richard E. Keating bought airline tickets for a party of four to circle the world twice on commercial airliners. Each party consisted of Hafele, Keating, and two passengers named “Mr. Clock.”

The guests were cesium-beam atomic clocks. The researchers chaperoned the timepieces once eastward around the world and once westward. Then they compared the traveling clocks with one that had remained at the United States Naval Observatory.

The results were published in Science the following year. The clocks had been found to disagree, demonstrating the effects of kinematic and gravitational time dilation.

The total cost of the effort was $8,000. It’s been called one of the most inexpensive tests ever conducted of Einstein’s relativity.

Cockatoos in Sydney have mastered a five-step process for opening the lids of trash bins to reach the food inside.

“It was so exciting to observe such an ingenious and innovative way to access a food resource, we knew immediately that we had to systematically study this unique foraging behavior,” wrote behavioral ecologist Barbara Klump.

The birds learn the technique from one another, and cockatoos in different regions have worked out different techniques. Before 2018, the behavior had been reported in only three suburbs, but by the end of 2019 the number had reached 44.

“These results show the animals really learned the behavior from other cockatoos in their vicinity,” Klump wrote.

(Barbara C. Klump et al. “Innovation and Geographic Spread of a Complex Foraging Culture in an Urban Parrot,” Science 373:6553 [2021], 456-460.) (Thanks, Sharon.)