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Math question re Pi

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

  1. durangodawood

    durangodawood Dis Member

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    Why is the convention to express Pi in terms of the diameter rather than the radius? Arbitrary? Some good reason?
     
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  2. OldWiseGuy

    OldWiseGuy Wake me when it's soup. Supporter

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    Pi r square makes no sense because everyone knows that pi r round. ^_^
     
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  3. Speedwell

    Speedwell Well-Known Member

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    The only reason I can think of is that the diameter of a circular object is a straight line thus more easily measurable and more likely to be known than the circumference.
     
  4. OldWiseGuy

    OldWiseGuy Wake me when it's soup. Supporter

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    But seriously, from a practical point of view you generally need to first know the diameter in order to determine the radius.
     
  5. OldWiseGuy

    OldWiseGuy Wake me when it's soup. Supporter

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    I hope this isn't going to the controversy over the measurement of the laver in 1Kings again. :doh:
     
  6. chevyontheriver

    chevyontheriver Well-Known Member Supporter

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    What would be the creationist point of view regarding pi?
     
  7. OldWiseGuy

    OldWiseGuy Wake me when it's soup. Supporter

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    3.14159265
     
  8. durangodawood

    durangodawood Dis Member

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    No laver palaver please!
     
  9. Lazarus Short

    Lazarus Short Well-Known Member

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    How about the Flat Earth view on Pi?
     
  10. durangodawood

    durangodawood Dis Member

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    No flat chat please!
     
  11. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    I believe that the OP means, "Why diameter and not radius?"

    I don't have a definitive answer, but I would guess that diameter was more important to builders, and was brought into analytical geometry a later time.

    (Notice that radians are based on radius rather than diameter.)
     
  12. durangodawood

    durangodawood Dis Member

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    Oh I know!

    If we used the radius, then Pi day would land on June 28.... but thats already Perfect Number Day.
     
  13. Aussie Pete

    Aussie Pete Well-Known Member Supporter

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    I just like my pi warmed up.
     
  14. Lazarus Short

    Lazarus Short Well-Known Member

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    [​IMG]
     
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  15. durangodawood

    durangodawood Dis Member

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    Then it expands to as much as 3.5 and all the wheels get wobbly.
     
  16. bekkilyn

    bekkilyn Contemplative Christian Supporter

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    My thought is that the formula uses in terms of diameter instead of radius because it is a less complex formula that eliminates the possibility of error. For example, if pi is the ratio of the circumference to the diameter, c/d, you could substitute numbers for c and d and get the same result.

    However, if you instead used the ratio of the circumference to twice the radius and used c/2r, then you may risk not always getting the same result as someone could introduce an error by using (c/2)r instead of c/(2r).

    The ratio of c/d is always clear.

    (There may also be something in Archimedes proof that makes diameter a better choice than ratio, but I haven't studied it.)
     
  17. OldWiseGuy

    OldWiseGuy Wake me when it's soup. Supporter

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    Pi x r/squared is the formula for the area of a circle.

    Pi x D is the formula for the circumference of a circle.

    Two entirely different measurements.
     
  18. Knee V

    Knee V It's phonetic.

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    Convention has us express things in the simplest terms possible. We could say that Pi = C/2r, but since 2r = d, it is simpler to say that Pi = C/d. Similarly, we could say that A = Pi * (d/2)^2, but it is simpler to say that A = Pi * r^2.

    In short, we express things as simply as possible. In some contexts that means we use r, and in some contexts we use d; whichever is simpler.
     
  19. durangodawood

    durangodawood Dis Member

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    Forget the 2 factor. Pi would be c/r =6.28ish.
     
  20. Sabertooth

    Sabertooth Repartee Animal: Quipping the Saints! Supporter

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    Not entirely different, since D = 2r.
     
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