Understanding the Physical Meaning of Pi in a Circle

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In summary, the conversation discusses the physical meaning of π in a circle. It is mentioned that π is a finite number, not infinite, and its decimal representation requires an infinite number of digits due to it being an irrational number. It is also noted that π represents the ratio of a circle's circumference to its diameter.
  • #1
akashpandey
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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.
 
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  • #2
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## ?
 
  • #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.
 
  • #4
akashpandey said:
pi have infinite value

##\pi## doesn't have infinite value, its a finite number and its fractional part can be expressed by an infinite sequence of numbers ...
 
  • #5
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 :)
 
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  • #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?
 
  • #7
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.
 
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  • #8
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.
 
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  • #9
HallsofIvy said:
How we can or cannot represent numbers in a particular "numeration system" says little about the properties of the numbers themselves.
Except for primes...
 
  • #10
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?
 
  • #11
HallsofIvy said:
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?
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.
 
  • #12
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.
 
  • #13
I can't understand hallsoflvy.
please understand with an example or in more clear way please.
 
  • #14
akashpandey said:
I can't understand hallsoflvy.
please understand with an example or in more clear way please.
HallsOfIvy made three posts in this thread. What part of what he said don't you understand?
 
  • #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
 
  • #16
sorrry my mistake
.
 
  • #17
I don't under the whole part.
please clear it in more easy way or with an example.
 
  • #18
##\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.

akashpandey said:
as we know that
circumference/diameter= π .
so how π has physical meaning in circle.
as it condstant.
The meaning is that in every circle, the ratio of the circumference to the diameter is always the same, ##\pi##.
 
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  • #19
You can interpret ##\pi## as the measure the flat angle.
 
  • #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?
 
  • #21
The ratio of a circle's circumference to its diameter is a physical quantity that is independent of the numerical representation. It is not rational in any number system. There are no integers, n & m where n*diameter = m*circumference.
 
  • #22
what?
 
  • #23
akashpandey said:
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?
Suppose you had a length of 314,159 diameters, end-to-end, and 100,000 circumferences end-to-end. The first length would be just short of the second length, but adding one more diameter to the first would make it longer than the second.
 
  • #24
akashpandey said:
what?
Sorry. I was replying to part of an earlier post:
HallsofIvy said:
How we can or cannot represent numbers in a particular "numeration system" says little about the properties of the numbers themselves.
This is true, but I think that the property of "rational" is not dependent on the base of a number system.
 
  • #25
akashpandey said:
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?
You have rulers with a length of 1 meter, and you want to measure your own height. How many rulers do you need?
Well, you are probably taller than a single ruler but not as tall as two rulers: your height is between 1 and 2 meters. Is there any interpretation problem with that?A comment on the decimal expansion: it is not terminating, but that is nothing special. If you express 1/3 in the decimal system, it is not terminating either: 1/3=0.33333...
It just has a pattern to the digits while the decimal digits of pi do not have a pattern.
 
  • #26
akashpandey said:
so we need 3.1425 arcs equal to measure of diameter to acquire a circle.
##\pi## is about 3.1416, not 3.1425. The circumference of a circle is exactly ##\pi## times the diameter of the circle.
akashpandey said:
so how I interpret last part of π i.e .14259 and so on in a circle?
??
It is what it is. In SI units, a one kilogram mass here on Earth has a weight of 9.8 Newtons. How do you interpret the .8 part? Because of the units chosen, that's how it turned out. For a circle, the extra .1416 (approx.) is what you need to get the proper relationship between the circumference and the diameter.
 
  • #28

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  • #30
yes .14159 and so on :nb) .
please can you explain ?
 
  • #31
akashpandey said:
yes .14159 and so on :nb) .
please can you explain ?

What exactly do you want explained? Have you understood anything that's been said in this thread so far?
 
  • #33
akashpandey said:
what is exact measurement of that last part since the measurement of that last part is .142 so on is infinite so its length is also .142 and so on

The exact length is three less than pi: π-3 = 0.14159...
 
  • #34
but how the length .142 is exact??
 
  • #35
means .142...
 

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