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I Π in the circle?

  1. Mar 4, 2016 #1
    I want to know that how to imply π in a circle.
    as we know that
    circumference/diameter= π .
    so how π has physical meaning in circle.
    as it condstant.
     
  2. jcsd
  3. Mar 4, 2016 #2

    BvU

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    Sorry, the question isn't clear to me. As you state, ##\pi## is the number of diameters a wheel moves forward with one revolution. What other physical meaning would you like to attribute to ##\pi## ?
     
  4. Mar 4, 2016 #3
    example.
    resistance is directly proportional to length and rho is proportionality constant an it different for different material.
    as same as .
    the π is constant so how I use this constant in the circle
    and also pi have infinite value so the area and circumference has infinite desimal value.
     
  5. Mar 4, 2016 #4

    Ssnow

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    ##\pi## doesn't have infinite value, its a finite number and its fractional part can be expressed by an infinite sequence of numbers ...
     
  6. Mar 4, 2016 #5

    ProfuselyQuarky

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    Well, I don't entirely understand your question, but here's how π is related to a circle in a physical sense:

    π equals the circumference divided by the diameter. So, ultimately, you have to "wrap around" the diameter of the circle π times. You need 3.1459 (and so on) arcs equal to the measure of the diameter to acquire the circumference of the circle.

    And, by the way, π does not have an infinite value, as Ssnow said, or else it would not be nearly so useful and it would be called infinity :)
     
    Last edited: Mar 4, 2016
  7. Mar 4, 2016 #6
    means that if π has infite no. of fraction than we have to take arc which has infinite no. of desimals .
    so their no perfect circle ever???
     
  8. Mar 4, 2016 #7

    ProfuselyQuarky

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    No, infinite digits after the decimal is not the same as a never-ending value. Just because the decimal value of π is non-terminating, it doesn't mean that π itself is infinite. We could approximate π to 22/7, but the quotient of that fraction does not give us every decimal value of π, thus making π irrational. That's all. Of course, there are perfect circles.
     
    Last edited: Mar 4, 2016
  9. Mar 4, 2016 #8

    HallsofIvy

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    You are failing to distinguish between mathematics and the way we represent mathematics. [itex]\pi[/itex] is a number, no different from any other number. One of the many applications of [itex]\pi[/itex] is that it happens to be the ratio of the circumference of a (mathematical) circle to its diameter. It is probably just a minor difficulty with language translation but [itex]\pi[/itex] is NOT "infinite" nor does it have "an infinite no. of fraction" nor does it have "an infinite no of decimals". It is has, rather, "an non-terminating decimal representation". But, as I said before, that is just a matter of how we represent it in a "base 10 place order numeration system". Since [itex]\pi[/itex] is an irrational number it cannot be represented in terms of integers which is what you seem to want to do. But there is nothing at all odd about that nor does it mean that there is no "perfect circle". How we can or cannot represent numbers in a particular "numeration system" says little about the properties of the numbers themselves.
     
  10. Mar 4, 2016 #9

    Svein

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    Except for primes...
     
  11. Mar 4, 2016 #10

    HallsofIvy

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    The prime number, 7, can be represented as "7" in base 10, obviously, "12" in base 5, "13" in base 4, "21" in base 3, etc. How do those representations show that the number is prime?
     
  12. Mar 4, 2016 #11

    Svein

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    No number representation shows that a number is prime. What I said (and meant) is that the "prime-ness" of a number is independent of the number representation.
     
  13. Mar 4, 2016 #12

    HallsofIvy

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    Ah. I suspected that. What I initially said was "How we can or cannot represent numbers in a particular "numeration system" says little about the properties of the numbers themselves." So what I was talking about was NOT whether numbers are or are not prime but whether or not their representation in a particular numeration system tells us that.
     
  14. Mar 4, 2016 #13
    I can't understand hallsoflvy.
    please understand with an example or in more clear way please.
     
  15. Mar 5, 2016 #14

    Mark44

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    HallsOfIvy made three posts in this thread. What part of what he said don't you understand?
     
  16. Mar 5, 2016 #15
    It is probably just a minor difficulty with language translation but π" role="presentation" style="display: inline-block; line-height: 0; font-size: 18.08px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; font-family: 'PT Sans', san-serif; position: relative;">ππ is NOT "infinite" nor does it have "an infinite no. of fraction" nor does ithave "an infinite no of decimals". It is has, rather, "an non-terminating decimal representation". But, as I said before, that is just a matter of how we represent it in a "base 10 place order numeration system". Since π" role="presentation" style="display: inline-block; line-height: 0; font-size: 18.08px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; font-family: 'PT Sans', san-serif; position: relative;">ππ is an irrationalnumber it cannot be represented in terms of integers which is what you seem to want to do. But there is nothing at all odd about that nor does it mean that there is no "perfect circle". How we can or cannot represent numbers in a particular "numeration system" says little about the properties of the numbers themselves..



    this part
     
  17. Mar 5, 2016 #16
    sorrry my mistake
    .
     
  18. Mar 5, 2016 #17
    I don't under the whole part.
    please clear it in more easy way or with an example.
     
  19. Mar 5, 2016 #18

    Mark44

    Staff: Mentor

    ##\pi## is a number between 3 and 4, which means that it's not infinite. It is irrational, so its decimal representation requires an infinite number of digits, which for most people is a matter of little concern. We can approximate it with, 3.14 or 3.1416 or 3.141592, or with as many places after the decimal point as are required for the accuracy we need.

    The meaning is that in every circle, the ratio of the circumference to the diameter is always the same, ##\pi##.
     
  20. Mar 5, 2016 #19

    Ssnow

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    You can interpret ##\pi## as the measure the flat angle.
     
  21. Mar 7, 2016 #20
    so we need 3.1425 arcs equal to measure of diameter to acquire a circle.

    so how I interpret last part of π i.e .14259 and so on in a circle????
     
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