Beautiful. In northern climes, let it run a bit…good for you.
Sorry about the bizarre name…
http://www.afuckingrainbow.com/
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Now this is different…
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The opening chord to A Hard Day’s Night is also famous because for 40 years, no one quite knew exactly what chord Harrison was playing. Musicians, scholars and amateur guitar players alike had all come up with their own theories, but it took a Dalhousie mathematician to figure out the exact formula….
Four years ago, inspired by reading news coverage about the song’s 40th anniversary, Dr. Brown decided to try and see if he could apply a mathematical calculation known as Fourier transform to solve the Beatles’ riddle. The process allowed him to decompose the sound into its original frequencies using computer software and parse out which notes were on the record.
It worked, up until a point: the frequencies he found didn’t match the known instrumentation on the song. “George played a 12-string Rickenbacker, Lennon had his six string, Paul had his bass… none of them quite fit what I found,” he explains. “Then the solution hit me: it wasn’t just those instruments. There was a piano in there as well, and that accounted for the problematic frequencies.”
Dr. Brown deduces that another George - George Martin, the Beatles producer - also played on the chord, adding a piano chord that included an F note impossible to play with the other notes on the guitar. The resulting chord was completely different than anything found in the literature about the song to date, which is one reason why Dr. Brown’s findings garnered international attention. He laughs that he may be the only mathematician ever to be published in Guitar Player magazine.
Thought you’d want to know
The number pi is the ratio between the circumference of a circle and its diameter. It’s approximately equal to 3.14159265, although the digits go on forever.
Some mathematicians are obsessed with computing pi to more and more digits. In the year 1610, a German mathematician computed pi to 35 digits. In 1789, a Slovene mathematician computed pi to 140 digits. This was all done by hand, in poorly heated houses.
An English amateur mathematician spent 20 years calculating pi to 707 digits, finishing in 1873. 71 years later, it was discovered that he had made a mistake at the 528th digit, and all the digits following it were wrong.
In 2002, frantic Japanese mathematicians used a supercomputer to accurately compute pi to 1,241,100,000,000 digits.
Based on all this effort, you might assume that it’d be useful to know a trillion digits of pi. However, if you had a circle the size of the observable universe, and you wanted to compute its circumference with an accuracy equal to the size of a proton, the number of digits of pi that you’d need is only 43.
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