A bigger piece of the pi: Finding the 100-trillionth digit
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The Keyword[^]:
A few months ago, on an average Tuesday morning in March, I sat down with my coffee to check on the program that had been running a calculation from my home office for 157 days
Spoiler alert: it's a '0'
"I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes '999999', so that I could recite it out loud, come to those six 9's, and then impishly say, 'and so on!'" - Douglas Hofstadter (and similar from Feynmann) edit: Made it more obvious that it was a quote - I wouldn't memorize pi beyond 3, myself ;P
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The Keyword[^]:
A few months ago, on an average Tuesday morning in March, I sat down with my coffee to check on the program that had been running a calculation from my home office for 157 days
Spoiler alert: it's a '0'
"I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes '999999', so that I could recite it out loud, come to those six 9's, and then impishly say, 'and so on!'" - Douglas Hofstadter (and similar from Feynmann) edit: Made it more obvious that it was a quote - I wouldn't memorize pi beyond 3, myself ;P
Kent Sharkey wrote:
I myself once learned 380 digits of π,
:wtf: :wtf: :wtf: :omg: :omg: :omg: I have never gone beyond the 3.141592 (and I have checked it out before submitting just to be sure :rolleyes: :doh: ...)
M.D.V. ;) If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about? Help me to understand what I'm saying, and I'll explain it better to you Rating helpful answers is nice, but saying thanks can be even nicer.
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The Keyword[^]:
A few months ago, on an average Tuesday morning in March, I sat down with my coffee to check on the program that had been running a calculation from my home office for 157 days
Spoiler alert: it's a '0'
"I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes '999999', so that I could recite it out loud, come to those six 9's, and then impishly say, 'and so on!'" - Douglas Hofstadter (and similar from Feynmann) edit: Made it more obvious that it was a quote - I wouldn't memorize pi beyond 3, myself ;P
Douglas Hofstadter wrote:
I myself once learned 380 digits of π, when I was a crazy high-school kid.
:omg: 'crazy' is definitely NOT an overstatement.
"the debugger doesn't tell me anything because this code compiles just fine" - random QA comment "Facebook is where you tell lies to your friends. Twitter is where you tell the truth to strangers." - chriselst "I don't drink any more... then again, I don't drink any less." - Mike Mullikins uncle
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The Keyword[^]:
A few months ago, on an average Tuesday morning in March, I sat down with my coffee to check on the program that had been running a calculation from my home office for 157 days
Spoiler alert: it's a '0'
"I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes '999999', so that I could recite it out loud, come to those six 9's, and then impishly say, 'and so on!'" - Douglas Hofstadter (and similar from Feynmann) edit: Made it more obvious that it was a quote - I wouldn't memorize pi beyond 3, myself ;P
They're all wrong after the first wrong one.
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The Keyword[^]:
A few months ago, on an average Tuesday morning in March, I sat down with my coffee to check on the program that had been running a calculation from my home office for 157 days
Spoiler alert: it's a '0'
"I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes '999999', so that I could recite it out loud, come to those six 9's, and then impishly say, 'and so on!'" - Douglas Hofstadter (and similar from Feynmann) edit: Made it more obvious that it was a quote - I wouldn't memorize pi beyond 3, myself ;P
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The Keyword[^]:
A few months ago, on an average Tuesday morning in March, I sat down with my coffee to check on the program that had been running a calculation from my home office for 157 days
Spoiler alert: it's a '0'
"I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes '999999', so that I could recite it out loud, come to those six 9's, and then impishly say, 'and so on!'" - Douglas Hofstadter (and similar from Feynmann) edit: Made it more obvious that it was a quote - I wouldn't memorize pi beyond 3, myself ;P
My high school teacher had taught me this: "How I wish I could recollect of circle round the exact relation Archimede unwound". Counting the number of letters, we get 3.1415926535897 Note that it is Archimede and not Archimedes - the name is modified to suit the Pi value.
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I think I will keep my PI mnemonic 113355, as 355/113 is a rather good approximation which fit my needs.
Patrice “Everything should be made as simple as possible, but no simpler.” Albert Einstein
:thumbsup: An accuracy of 10-7 is good enough to draw a circle of radius 10m to an accuracy of 1 micron. Plenty for almost any earthly engineering tasks...
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows. -- 6079 Smith W.
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The Keyword[^]:
A few months ago, on an average Tuesday morning in March, I sat down with my coffee to check on the program that had been running a calculation from my home office for 157 days
Spoiler alert: it's a '0'
"I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes '999999', so that I could recite it out loud, come to those six 9's, and then impishly say, 'and so on!'" - Douglas Hofstadter (and similar from Feynmann) edit: Made it more obvious that it was a quote - I wouldn't memorize pi beyond 3, myself ;P
The approximation I was taught to use in school back in the early 80s was 22/7, not great but good enough for the calculatorless mathematics exams at the time.
“That which can be asserted without evidence, can be dismissed without evidence.”
― Christopher Hitchens
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The approximation I was taught to use in school back in the early 80s was 22/7, not great but good enough for the calculatorless mathematics exams at the time.
“That which can be asserted without evidence, can be dismissed without evidence.”
― Christopher Hitchens
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The Keyword[^]:
A few months ago, on an average Tuesday morning in March, I sat down with my coffee to check on the program that had been running a calculation from my home office for 157 days
Spoiler alert: it's a '0'
"I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes '999999', so that I could recite it out loud, come to those six 9's, and then impishly say, 'and so on!'" - Douglas Hofstadter (and similar from Feynmann) edit: Made it more obvious that it was a quote - I wouldn't memorize pi beyond 3, myself ;P
During one afternoon spent sitting in the car at some school sports nonsense, I remembered it as 3.141592658579. Checking now, I see that I'm fairly close. 3.1415926535897 Still forget what I did with the whatsit from yesterday though, a period roughly 10,950 times shorter.. :laugh: :laugh:
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The Keyword[^]:
A few months ago, on an average Tuesday morning in March, I sat down with my coffee to check on the program that had been running a calculation from my home office for 157 days
Spoiler alert: it's a '0'
"I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes '999999', so that I could recite it out loud, come to those six 9's, and then impishly say, 'and so on!'" - Douglas Hofstadter (and similar from Feynmann) edit: Made it more obvious that it was a quote - I wouldn't memorize pi beyond 3, myself ;P
Years ago (I believe it was in the late 1970s), University of Bergen, Norway, ran a huge IBM mainframe. The IT department had a professor teaching a course in error propagation, and in preparing the course material, he saw that the error in calculating the arctan(), which may be a little nasty for extreme values, was higher than one should expect, given 32 bits of precision. As a good researcher should do, he set out to find the explanation. To make a long story short: In the old days, you didn't repeat calculations unless needed. For the old IBM 709, the binary representation of pi had been calculated, and the hex bit pattern was copied whenever needed. For the IBM 7090 Fortran library, the hex was copied without any change. 709/7090 were 36 bit machines. The 360 series were 32 bits. So when the Fortran library was ported, the least significant, last four bits, i.e. the last hex digit, of the pi constant, was chopped off. No one considered rounding. The chopped-off bits were significantly above '.5' (or 1000 as a bit pattern), so the last retained bit should have been rounded up to 1. It remained at 0. No updates to the Fortran library was required (or, at least the pi constant was unchanged), and later to 303x. Once the least significant pi bit was correctly rounded up to 1, the error in the arctan() function dropped to the level predicted by the theoretical analysis.
