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Math question re Pi

Discussion in 'The Kitchen Sink' started by durangodawood, Mar 15, 2020.

  1. bekkilyn

    bekkilyn Contemplative Christian Supporter

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    And how would you mathematically prove that Pi is really the ratio of the circumference to the radius instead of the ratio of the circumference to the diameter? Especially since the radius cannot be equal to the diameter.
     
  2. durangodawood

    durangodawood Dis Member

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    D is just 2r. They are completely interchangeable for the purpose of deriving Pi.
     
  3. durangodawood

    durangodawood Dis Member

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    Because D is precisely equal to 2r. The conversion could not be more simple.
     
  4. durangodawood

    durangodawood Dis Member

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    In terms of r Pi =6.28... is exactly as simple as Pi =3.14... in terms of D. The complexity either way is identical.
     
  5. bekkilyn

    bekkilyn Contemplative Christian Supporter

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    You said to forget the 2 and thus change Pi to 6.28ish. How would you mathematically prove that 3.14ish is equivalent to 6.28ish and that r is equal to 2r since the 2 factor doesn't matter?

    If we forget the 2, then we no longer have c/(2r) but instead c/r which is not at all the same formula.
     
  6. bekkilyn

    bekkilyn Contemplative Christian Supporter

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    If you divide the denominator by 2, then you must divide the numerator by two, so to get rid of the 2 in the denominator, you would need to write the ratio as (c/2)/(2r/2) which simplifies to (c/2)/r which then simplifies right back to c/(2r).
     
  7. Knee V

    Knee V It's phonetic.

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    I see what you're saying now.

    Maybe the diameter is more of a "real thing" than the radius?
     
  8. OldWiseGuy

    OldWiseGuy Wake me when it's soup. Supporter

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    I meant the measurements have different purposes. For instance the circumference of a barrel isn't necessary to calculate it's volume.
     
  9. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    It would be, if you knew where A = pi x r^2 came from.

    Area of a Circle
     
  10. OldWiseGuy

    OldWiseGuy Wake me when it's soup. Supporter

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    Why make it more complicated than it needs to be?

    Some people use a hammer spinning awkwardly through the air to demonstrate that the center of balance of such an object forms a smooth ark.

    I use it to drive nails. :D
     
    Last edited: Mar 15, 2020
  11. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    That is where A = pi x r^2 came from. It riffs on circumference. (Knowing that, we just commit it to memory.)

    Your barrel calculation still uses circumference in the process. It is just contained within the rote formula.
     
  12. Occams Barber

    Occams Barber Newbie Supporter

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    I'm used to seeing circumference expressed as both *D and 2*R. If anything, 2*R is the more conventional.

    Then again I do live in an upside-down country. :)

    OB
    (Edit: *Oooops - my pasted Pi's have fell off)

    OB
     
  13. Occams Barber

    Occams Barber Newbie Supporter

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    How can you calculate the volume of a barrel without using the circumference?

    OB
     
  14. essentialsaltes

    essentialsaltes Stranger in a Strange Land

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    It is entirely arbitrary.

    The use of the Greek letter pi for this ratio is really only a few centuries old. But once that particular standard was chosen and populartized, the arbitrary choice became fixed.

    The concept of a fixed ratio for circles is thousands of years older and developed independently in several cultures. Some defined it differently.
     
  15. OldWiseGuy

    OldWiseGuy Wake me when it's soup. Supporter

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    Volume = height x Pi x r squared.

    No circumference (Pi x D) needed.
     
  16. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    Pi comes from c/d.

    Without pi, volume = height x (circumference/diameter) x (radius, squared)
     
  17. OldWiseGuy

    OldWiseGuy Wake me when it's soup. Supporter

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    But we don't need to reinvent Pi, it's a 'given'.
     
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