All about Pi

Discussion in 'Science' started by HereWeGoAgain, Mar 14, 2018.

  1. HereWeGoAgain

    HereWeGoAgain Banned

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    Mathematician: Pi R Squared
    Baker: No, pies are round.

    What do you have if you divide the sun's circumference by it's diameter? Pi in the sky!

    March 14, 3/14 is Pi day. It is the day Stephen Hawking died and Albert Einstein's birthday.

    It is the most recognized mathematical symbol

    Politicians once tried to define its exact value by passing a law.

    Pi is the ratio of a circle's circumference to it's diameter.

    Pi has been calculated to over 1 trillion digits, but never repeats. It is endless.

    It has been memorized to over 65,000 digits

    -Around 2000 B.C., Babylonians established the constant circle ratio as 3 1/8 or 3.125. The ancient Egyptians arrived at a slightly different value of 3 1/7 or 3.143.*

    -One of the earliest known records of pi was written by an Egyptian scribe named Ahmes (c. 1650 B.C.) on what is now known as the Rhind Papyrus. He was off by less than 1% of the modern approximation of pi (3.141592).*

    -Plato (427-348 B.C.) supposedly obtained for his day a fairly accurate value for pi: √2 + √3 = 3.146.*

    -The father of calculus (meaning "pebble used in counting," from calx or "limestone"), Isaac Newton, calculated pi to at least 16 decimal places.*

    -William Jones (1675-1749) introduced the symbol "π" in the 1706, and it was later popularized by Leonhard Euler (1707-1783) in 1737.*
    https://www.networkworld.com/articl...s-about-pi-that-you-probably-didn-t-know.html

    The way a river meanders is described by its sinuosity; the length of its winding path divided by the distance from the source to the ocean as measured in a straight line. Strange as it may be, the average river has a sinuosity of around 3.14, according to the journal Science.

    among a collection of random whole numbers, the probability that any two numbers have no common factor — that they are "relatively prime" — is equal to 6/π^2

    pi's ubiquity goes beyond math. The number crops up in the natural world, too. It appears everywhere there's a circle, of course, such as the disk of the sun, the spiral of the DNA double helix, the pupil of the eye, the concentric rings that travel outward from splashes in ponds. Pi also appears in the physics that describes waves, such as ripples of light and sound. It even enters into the equation that defines how precisely we can know the state of the universe, known as Heisenberg's uncertainty principle.

    3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049 9510597317328160963185950244...
     
    Last edited: Mar 14, 2018
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  2. HereWeGoAgain

    HereWeGoAgain Banned

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    Pi is an exponent in what has been called [Feynman] the most beautiful equation in all of mathematics. It is definitely my personal favorite.

    Euler's identity

    [​IMG]
     
    Last edited: Mar 15, 2018
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  3. HereWeGoAgain

    HereWeGoAgain Banned

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  4. HereWeGoAgain

    HereWeGoAgain Banned

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    Pi can be expressed as an infinite series

    [​IMG]

    This is derived from the inverse tangent expansion
    [​IMG]
     
    Last edited: Mar 16, 2018
  5. HereWeGoAgain

    HereWeGoAgain Banned

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  6. Brett Nortje

    Brett Nortje Well-Known Member

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    Pi is used in engineering, yes? If you think about it, is it twenty two divided by seven, of course.

    But, what angle comes to "twenty two?" Seeing as how it is the value of the circle divided by two, a full circle divided by four would be better, of course? This would leave you with a big yummy zero where the five is, 'cutting it short' and making it a whole number, before the zero.

    But, let's get into some pi theory!

    Pi, why is it there? working with decimals is tedious and hard to remember, how about we expand our view before we come up with an answer? Pi is a value for the "circumference to the diameter," yes? This means, in other words, that it is the whole circle's outside - 360 degrees - divided by the inside to the centre point - zero degrees.

    ~ If we were to be honest, we would say that it is quite simple the way I put it, and, the way the greats put it it makes you want to do something else like mow the lawn or clean the toilet, yes?

    Now, if we were to use a right angle cross section, we would find it comes to 360 degrees by ninety degrees, coming to four, yes? This is not the case though, and, the right way to approach this, with a baseless formula to get the same answer - to see what wanders through the minds of various greats - is to find the calculus formula for pi. This could be where we estimate that it would be 110 degrees, or, 111 degrees, yes? This would be the outside of the angle of pi, far more commonly useful than some gibberish with decimal points that you need to convert into an angle!
     
  7. HereWeGoAgain

    HereWeGoAgain Banned

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    That is only an approximation.
     
  8. Diablo

    Diablo Well-Known Member

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    What do you call a funny snake that can climb mountains?

    A Mounty πthon.
     
    Last edited: Mar 18, 2018
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  9. fmw

    fmw Well-Known Member

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    This is all just pi in the sky.
     
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  10. HereWeGoAgain

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  11. HereWeGoAgain

    HereWeGoAgain Banned

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    Infinite products
    [​IMG] (Euler)
    where the numerators are the odd primes; each denominator is the multiple of four nearest to the numerator.
    [​IMG] (see also Wallis product)
    Viète's formula:
    [​IMG]
     
    Last edited: Mar 22, 2018
  12. HereWeGoAgain

    HereWeGoAgain Banned

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    Last edited: Mar 23, 2018
  13. Space_Time

    Space_Time Well-Known Member

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  14. HereWeGoAgain

    HereWeGoAgain Banned

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  15. kazenatsu

    kazenatsu Well-Known Member Past Donor

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    negative one raised to the power of pi
    (-1)^π

    As you can see from that infinite sum series, pi can be neither even nor odd.
     
    Last edited: Mar 21, 2019

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