Times four, for the four corners of the Earth, so 192 hours.
The sum of all the positive integers between 1 and n is the nth triangular number T_n. The simple formula is T_n=\frac{n(n+1)}2. An elementary proof is to arrange the numbers 1 … n in a line and then n … 1 below it. Add them up and you get n terms each adding to n+1. So n(n+1). Since each number has appeared twice, once in each row, divide by 2 to get T_n. These are called triangular numbers because you can think of them arrayed in a triangle. Think of a pool rack of 15=T_5 balls.
Incidentally, every number is the sum of three triangular numbers, just as every number is the sum of four squares (and five pentagonal numbers and so on).
Thank you! Makes perfect sense now.
Yes, the equations balance. Have you seen the algorithm elsewhere?
No, but it is too obvious to be new.
OK, I should have known - sorry, not a mathematician.
An interesting random fact I stumbled across last night is that triangular numbers are the products of two integer sequences: 1 3 3 5 5 7… and 1 1 2 2 3 3 4 4…
1 x 1 = 1
1 x 3 = 3
2 x 3 = 6
2 x 5 = 10
3 x 5 = 15
3 x 7 = 21
4 x 7 = 28
4 x 9 = 36
5 x 9 = 45
There’s a scene in the 1946 film It’s a Wonderful Life where a retractable basketball court opens up to reveal a hidden swimming pool beneath it. Today I learned it was filmed at Beverly Hills High School, and that the basketball court and pool still exist.
Today I learned that chicken hens only have one working ovary, and if the one that works stops working, the dormant one develops into an ovotestis and that this is why older hens who have stopped laying may grow spurs and a comb and start crowing.
Nature is weird and wonderful.
One of my hens did that a few years ago. If you didn’t know you would swear that she was a cockerel. Unfortunately it often leads to death within a few months. RIP Crackle.
I used to live very near MSP, but even though I live farther out this sound carries quite well in the cold. But, curiously, because of spending so much time with them as background noise, I learned to identify the lack of sound right before the deceleration groan hits my ears. For a while, it became my party trick to declare “Incoming” like Radar O’Reilly right before the deceleration Whuuuuh could be heard.
A few of our hens have transitioned in old age.
The band The Residents have a similar story. They sent a demo tape to a record company and didn’t list a band name. The rejection was sent to their address and addressed Residents. They ended up liking it and made it the name of the band.
That’s a right triangle, you idiot!
Not sure if it is fact or urban legend (I didn’t see it mentioned on their Wikipedia page) but supposedly The Police named the band on the advice of Stewart Copeland’s dad, who worked for the CIA. He told them that a sure-fire way to get record executives to call them back was to leave a message that “The Police want to talk to you.”
On Sunday I heard of Dave Godin for the first time – he was the central character in the expansion of Motown into the UK (and thence the world), and actually coined the name Tamla Motown, the brand used outside the US. He founded the (UK) Tamla Motown Appreciation Society and eventually became Motown’s UK consultant. He also coined the term Northern Soul, started the first shop in Europe specializing in black music, and introduced Mick Jagger to black music (which he later profoundly regretted).
”It was at Dartford Grammar School that I met Mick Jagger and introduced him to black music, I’m ashamed to say. It’s ironic that as a result of meeting me he’s where he is today." Godin played a minor role in the early jam sessions out of which the Rolling Stones emerged, but resented Jagger for what he saw as the Stones’ exploitation of black music.
…. At a recording of [TV show] Ready Steady Go! in 1964, Jagger [by that time already famous] asked Godin to introduce him to Marvin Gaye. “I told him to f*** off and introduce himself”, Godin recalled.
His work and influence is front and centre in the excellent new BBC documentary When Motown Came To Britain. Look out for it.
I’m slightly astonished that I had never heard of him. One obituary noted that his influence far exceeded his fame.
Wiki page:
And here’s a kind of memorial page with links, including those to obituaries in The Independant and The Guardian: Dave Godin
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In Rome, there’s a hill made up almost entirely of fragments of ancient Roman pottery.
In Berlin, the highest hill is made of piled up rubble from the ruins of the houses bombed in WWII: the Teufelsberg. 120 m over sea level, 80 m above the surroundling area, it covers an unfinished Nazi military-technical college (Wehrtechnische Fakultät). It was easier to cover it with debris than to demolish it. The US National Security Agency (NSA) built one of its largest listening stations atop the hill in 1963. It also had a 24 m long (79 ft) ski jump and in 1987 an alpine ski race was held on its slopes to mark the 750th anniversary of the foundation of Berlin. It was a short and boring race, but it was mainly meant as a political symbol.
That year the Tour de France also started in Berlin, in the French sector, of course.
Fresh Kills landfill on Staten Island was once the highest point on the eastern seaboard. It is now Fresh Kills park and has been lowered somewhat. NYC is exporting their solid waste to elsewhere.
I recently learned that the lid on the trash bins in some airplane bathrooms can be opened via a foot lever, saving your freshly washed hands from having to manually push down on said lid:
Sadly, I also recently learned that a particular type of plane I regularly fly on, the Airbus A330-200, does not have this feature.