Happy Pi Day Open Thread: Monday, March 14, 2016

Happy Pi Day

Today’s number is 14, but I’ll throw in some Pi first

Pi is sometimes approximated as 22/7, giving it a link to 14 via the link between 1/7 and 1/14 to be discussed later

BUT! Pi, like modern politics, is irrational , it never ends.

We learn circles as kids;

Circumference = 2 • π • radius = π • diameter

Circle Area = π • r² = ¼ • π • d²

sometimes also spheres

Sphere Surface Area = 4 • π • r² = π • d²

Sphere Volume = 4/3 • π • r³ = ( π •d³)/6

But think about music for a minute, all those nice waves in the air, and in the wires and the headphones and the speakers

Those are sine waves and have zero amplitude at points that are Pi units apart, such as at -2 π, -1 π, 0, π, 2 π, etc. where the peak height is one unit

In between, they have alternating maximum and minimum values of + or - one unit at points that are integer multiples of π/2, for instance, a maximum at -3π/2, a minimum at - π/2, a maximum at π/2, a minimum at 3π/2, etc

The Pythagoreans knew that harmonics were based on fractions, but never learned that sound itself was trigonometry (which they didn’t grok)

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14 is the product of 2 primes, 7 and 2

Alrighty. If 14 = 7 x 2, then x/14 = x/(7x2). As we learned in last Monday's Open Thread, fractions of the form x/7 where x is a whole number not a multiple of 7 or 999,999 have an interesting property. For any even numerator x, x/14 will factor down to (x/2)/7, so even fractions of the form x/14 have the same interesting property. Interestingly enough, heh, for odd numerators, x/14 has a variant of that property. Last Monday =http://caucus99percent.com/content/open-thread-monday-march-7-2016 crossposted towww.dailykos.com/...

Briefly, the fractional part of x/7 is the number sequence 142857 repeated endlessly in that order from a varying but determinable starting point within that series. Thus 1/7 = 0.142857142857..., 2/7 = 0.2857142857..., 3/7 = 0.42857142857..., etc. 2/14 = 1/7 = 0.142857, etc. When x/14 has an odd numerator, the 142857 repeat kicks in, but not necessarily in mid series as it does with x/7. Instead, 1/14, for example = 0.071428571... and 3/14 = 0.214285714..., 5/14 = 0.357142857... etc.

Cambrian animals of the genus Hallucinogenia (wikiCommons picture) had 14 legs.

Hallucinogenia

14 BCE was the Year of the Consulship of Crassus and Lentulus. Claudia Pulchra was born. She became the 3rd wife of Publius Quinctilius Varus. (Yep, that Varus again. This is the 3rd time he has popped up in a Monday Open Thread in the few months I've been doing them. One time for each legion he got annihilated.)

14 CE was the Year of the Consulship of Pompeius and Appuleius. On August 19, Caesar Augustus died. He was succeeded by Tiberius on September 18. He was also declared to be a god, but I don't know the date. Being a god was easier then - just die with a lot of fans. Augustus' grandson, Postumus Agrippa, was slain by his own guards on August 20, but that isn't why he was named Posthumus.

On this date in
1592	was the best correspondence to Pi in history - 3141592
1794	Eli Whitney got a patent for the cotton gin
1885	The Mikado was first publicly performed in London
1903	The Pelican Island Wildlife Refuge was established
1910	The Lakeview Gusher blew its top near Bakersfield. It is still the largest accidental spill in history,
1931	The first Indian talkie, Alam Ara, was released.
1943	The Krakow Ghetto was liquidated
1964	Jack Ruby was convicted of killing Lee Harvey Oswald
1978	Israeli Defense Forces invaded and occupied southern Lebanon
1994	Version 1.0.0 of the Linux kernel was released
2007	The first World Math(s) Day was celebrated. So Pi 2 U 2!

Born this day in
1681	Georg Philipp Telemann, a composer & music theorist
1804	Johann Strauss I, a composer & conductor
1820	Victor Emmanuel II, a King & The Father of Italy
1835	Giovanni Schiaparelli, an astronomer who is blamed for the Martian Canals silliness
1863	Casey Jones, an engineer for the Illinois-Central RR
1879	Albert Einstein, a patent clerk, engineer and scientist
1882	Wacław Franciszek Sierpiński, a mathematician & topologist
1887	Sylvia Beach, a publisher, founder of Shakespeare & Company
1912	Les Brown, a sax player, composer & bandleader
1914	Lee Hays, a singer & songwriter (The Almanac Singers & The Weavers)
1919	Max Shulman, an author & playwright
1920	Hank Ketcham, a cartoonist
1922	Les Baxter. a pianist & composer
1932	Mark Murphy, a singer
1933	Quincy Jones, a singer, songwriter, producer, & trumpet player
1943	Leroy Bonner, a guitarist, singer & producer
1945	Michael Martin Murphy a singer, guitarist & songwriter
1945	Walter Parazaider, a sax player (Chicago)
1951	Jerry Greenfield, an ice cream manufacturer
1954	Jann Brown a singer (Asleep at the Wheel)

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Died this day in
1471	Thomas Malory, an author
1823	John Jervis, 1st Earl of St Vincent, an admiral & politician
1883	Karl Marx, an author and philosopher
1973	Chic Young, a cartoonist
1976	Busby Berkeley, a choreographer & director
1977	Fannie Lou Hamer, an activist
1989	Edward Abbey, an author & activist who liked solitaire
2012	Eddie King, a guitarist, singer & songwriter