National π Day

Discussion in 'Off-Topic' started by Monster_Sparklez, Mar 14, 2019.

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  1. Monster_Sparklez
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    Monster_Sparklez Yee yee Bubba Premium Premium

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    Today is 3-14-19 Also known as National Pi Day
    For those who don't know, pi is used in math and is simply known as 3.14 ... But there's more
    One Million Digits of Pi – – Pi Day
    ^1 Million digits^
     
  2. ~Sky~
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    The next number is 2
     
  3. trin
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    trin beamer boy Premium

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    There’s an endless computer somewhere calculating pi
     
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  4. archerexpert777
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    archerexpert777 Senior Member

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    To whoever invented pi, I don't get how they come up with solving it in the first place. If they were going to measure the circumference of a circle, they'd use a rope and measure the length of the rope. Still amazes yet confuses me how someone found 3.14 and all those decimals as if they used calculus to find pi.
     
  5. Michael
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    Michael Super Moderator Staff Member

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    The derivation of pi is actually quite interesting; for much of history, pi was only known to an accuracy of a few decimal places. I believe that it was Archimedes who first developed a system for accurately approximating pi, by considering the perimeters of circumscribed and inscribed regular polygons, which gave upper and lower bounds to what the actual value of pi could be. Once the polygon gains enough sides, it ends up looking more and more like a circle, to the point where it can be used to approximate pi with quite a bit of accuracy.

    More than 500 years later, a mathematician named Liu Hui created an algorithm to approximate pi, using this same concept, allowing Zu Chongzhi, about 200 years later, to use this algorithm with a twelve thousand sided polygon, which was the most accurate approximation of pi until the early 15th century. After that, people began, quite rapidly, approximating pi with more and more accuracy. Infinite polynomial expansions of various functions also proved to be quite useful, as they could be used to approximate pi without the need for geometric interpretations, by using facts such as arcsin(1) = pi/2, and plugging the value of 1 into the polynomial expansion for arcsin, and multiplying by 2 to arrive at the approximate value. During the 20th century, people also began using computers to automate the process, allowing for even more precise approximations of pi.
     
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  6. archerexpert777
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    archerexpert777 Senior Member

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    Finally, the most interesting lecture <333333
     
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