Silly Question about $π$ [closed]
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In our junior classes, we learnt that $π$ is an irrational number. Now, also we know about rational numbers. So, if I say that I have a thread of 44cm long and we may convert it into a circle. Then how come we can say that our measure for the thread is correct. Also I may, then, assume that every measure is therefore not correct even that precise sample that has been kept as the standard unit 1 metre length scale. So is for the whole universe or any system. Is it correct? Any reviews?
Thanks for seeing this silly question! :)
irrational-numbers rational-numbers pi
asked Nov 26 at 17:58
jayant98
35614
closed as unclear what you're asking by Andrés E. Caicedo, Bungo, Mark Viola, Lord Shark the Unknown, Cesareo Nov 27 at 2:17
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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In our junior classes, we learnt that $π$ is an irrational number. Now, also we know about rational numbers. So, if I say that I have a thread of 44cm long and we may convert it into a circle. Then how come we can say that our measure for the thread is correct. Also I may, then, assume that every measure is therefore not correct even that precise sample that has been kept as the standard unit 1 metre length scale. So is for the whole universe or any system. Is it correct? Any reviews?
Thanks for seeing this silly question! :)
irrational-numbers rational-numbers pi
asked Nov 26 at 17:58
jayant98
35614
closed as unclear what you're asking by Andrés E. Caicedo, Bungo, Mark Viola, Lord Shark the Unknown, Cesareo Nov 27 at 2:17
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
I'd say you don't have enough measurement precision to answer the question.
– Adrian Keister
Nov 26 at 18:00
3
If the circumference of a circle is $44$, then its radius is $22/pi$.
– Berci
Nov 26 at 18:01
What does that mean? Please explain...
– jayant98
Nov 26 at 18:02
1
Physical measurements have little concern about rational vs. irrational - most are precise only to 10 decimal places or thereabouts.
– Hagen von Eitzen
Nov 26 at 18:02
1
A physical thread is not a mathematical line or circle: it is a complicated three-dimensional object. Look at it under a microscope and you'll see the complications. To say that it has a certain length, and that it preserves that length when you move it, is only an approximation.
– Robert Israel
Nov 26 at 18:08
|
show 3 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
In our junior classes, we learnt that $π$ is an irrational number. Now, also we know about rational numbers. So, if I say that I have a thread of 44cm long and we may convert it into a circle. Then how come we can say that our measure for the thread is correct. Also I may, then, assume that every measure is therefore not correct even that precise sample that has been kept as the standard unit 1 metre length scale. So is for the whole universe or any system. Is it correct? Any reviews?
Thanks for seeing this silly question! :)
irrational-numbers rational-numbers pi
asked Nov 26 at 17:58
jayant98
35614
In our junior classes, we learnt that $π$ is an irrational number. Now, also we know about rational numbers. So, if I say that I have a thread of 44cm long and we may convert it into a circle. Then how come we can say that our measure for the thread is correct. Also I may, then, assume that every measure is therefore not correct even that precise sample that has been kept as the standard unit 1 metre length scale. So is for the whole universe or any system. Is it correct? Any reviews?
Thanks for seeing this silly question! :)
irrational-numbers rational-numbers pi
irrational-numbers rational-numbers pi
asked Nov 26 at 17:58
jayant98
35614
asked Nov 26 at 17:58
jayant98
35614
asked Nov 26 at 17:58
jayant98
35614
asked Nov 26 at 17:58
jayant98
35614
asked Nov 26 at 17:58
jayant98
35614
35614
closed as unclear what you're asking by Andrés E. Caicedo, Bungo, Mark Viola, Lord Shark the Unknown, Cesareo Nov 27 at 2:17
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Andrés E. Caicedo, Bungo, Mark Viola, Lord Shark the Unknown, Cesareo Nov 27 at 2:17
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
I'd say you don't have enough measurement precision to answer the question.
– Adrian Keister
Nov 26 at 18:00
3
If the circumference of a circle is $44$, then its radius is $22/pi$.
– Berci
Nov 26 at 18:01
What does that mean? Please explain...
– jayant98
Nov 26 at 18:02
1
Physical measurements have little concern about rational vs. irrational - most are precise only to 10 decimal places or thereabouts.
– Hagen von Eitzen
Nov 26 at 18:02
1
A physical thread is not a mathematical line or circle: it is a complicated three-dimensional object. Look at it under a microscope and you'll see the complications. To say that it has a certain length, and that it preserves that length when you move it, is only an approximation.
– Robert Israel
Nov 26 at 18:08
|
show 3 more comments
I'd say you don't have enough measurement precision to answer the question.
– Adrian Keister
Nov 26 at 18:00
3
If the circumference of a circle is $44$, then its radius is $22/pi$.
– Berci
Nov 26 at 18:01
What does that mean? Please explain...
– jayant98
Nov 26 at 18:02
1
Physical measurements have little concern about rational vs. irrational - most are precise only to 10 decimal places or thereabouts.
– Hagen von Eitzen
Nov 26 at 18:02
1
A physical thread is not a mathematical line or circle: it is a complicated three-dimensional object. Look at it under a microscope and you'll see the complications. To say that it has a certain length, and that it preserves that length when you move it, is only an approximation.
– Robert Israel
Nov 26 at 18:08
I'd say you don't have enough measurement precision to answer the question.
– Adrian Keister
Nov 26 at 18:00
I'd say you don't have enough measurement precision to answer the question.
– Adrian Keister
Nov 26 at 18:00
3
3
If the circumference of a circle is $44$, then its radius is $22/pi$.
– Berci
Nov 26 at 18:01
If the circumference of a circle is $44$, then its radius is $22/pi$.
– Berci
Nov 26 at 18:01
What does that mean? Please explain...
– jayant98
Nov 26 at 18:02
What does that mean? Please explain...
– jayant98
Nov 26 at 18:02
1
1
Physical measurements have little concern about rational vs. irrational - most are precise only to 10 decimal places or thereabouts.
– Hagen von Eitzen
Nov 26 at 18:02
Physical measurements have little concern about rational vs. irrational - most are precise only to 10 decimal places or thereabouts.
– Hagen von Eitzen
Nov 26 at 18:02
1
1
A physical thread is not a mathematical line or circle: it is a complicated three-dimensional object. Look at it under a microscope and you'll see the complications. To say that it has a certain length, and that it preserves that length when you move it, is only an approximation.
– Robert Israel
Nov 26 at 18:08
A physical thread is not a mathematical line or circle: it is a complicated three-dimensional object. Look at it under a microscope and you'll see the complications. To say that it has a certain length, and that it preserves that length when you move it, is only an approximation.
– Robert Israel
Nov 26 at 18:08
|
show 3 more comments
3 Answers
3
active
oldest
votes
up vote
2
down vote
accepted
“In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities[1] asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.“ - https://en.wikipedia.org/wiki/Uncertainty_principle
So the question is not silly. Human measurements or those made by our machines, are not precise. See the above for the reason why.
Mathematics is precise.
answered Nov 26 at 18:04
John L Winters
849
add a comment |
up vote
1
down vote
A circle made of a material probably cannot exist, due to small scale physical issues that are mostly off topic here. Instead, in a semi-idealized way, you can imagine that you can really construct a regular polygon with an extremely large number of sides (in fact you cannot really do this either for the same reason as for the circle, but we have to idealize somewhere in order to do math). Taking the ratio of the perimeter of this polygon (which is your 44 cm) and the distance from the center to one of the vertices results in a rational approximation of $2pi$. Or, if you think from the point of view of math approximating physics rather than the other way around, $2pi$ is an approximation for these rational numbers.
In any case you've stumbled into the interesting fact that we can never really see an irrational number falling out of a physical measurement.
(As an aside, the meter isn't defined by an artifact, but rather through the definition of the second and a prespecified value for the speed of light in vacuum as measured in meters per second. This has been the case for several decades.)
answered Nov 26 at 18:04
Ian
67.3k25285
thanks for your answer. It very much cleared my doubt with such a simple explanation. I really appreciate your writing. Thanks again!
– jayant98
Nov 26 at 18:15
add a comment |
up vote
0
down vote
I think because the 44cm long thread is the radius of the circle. This is usually rational because you don't need $π$ in the measurement of the radius in a circle.
answered Nov 26 at 18:07
LukeyBear
33
2
In an idealized situation, if you wrapped a 44 cm long straight piece of thread into a circle shape, its perimeter would be 44 cm.
– Ian
Nov 26 at 18:13
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
“In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities[1] asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.“ - https://en.wikipedia.org/wiki/Uncertainty_principle
So the question is not silly. Human measurements or those made by our machines, are not precise. See the above for the reason why.
Mathematics is precise.
answered Nov 26 at 18:04
John L Winters
849
add a comment |
up vote
2
down vote
accepted
“In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities[1] asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.“ - https://en.wikipedia.org/wiki/Uncertainty_principle
So the question is not silly. Human measurements or those made by our machines, are not precise. See the above for the reason why.
Mathematics is precise.
answered Nov 26 at 18:04
John L Winters
849
add a comment |
up vote
2
down vote
accepted
up vote
2
down vote
accepted
“In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities[1] asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.“ - https://en.wikipedia.org/wiki/Uncertainty_principle
So the question is not silly. Human measurements or those made by our machines, are not precise. See the above for the reason why.
Mathematics is precise.
answered Nov 26 at 18:04
John L Winters
849
“In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities[1] asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.“ - https://en.wikipedia.org/wiki/Uncertainty_principle
So the question is not silly. Human measurements or those made by our machines, are not precise. See the above for the reason why.
Mathematics is precise.
answered Nov 26 at 18:04
John L Winters
849
answered Nov 26 at 18:04
John L Winters
849
answered Nov 26 at 18:04
John L Winters
849
answered Nov 26 at 18:04
John L Winters
849
849
add a comment |
add a comment |
up vote
1
down vote
A circle made of a material probably cannot exist, due to small scale physical issues that are mostly off topic here. Instead, in a semi-idealized way, you can imagine that you can really construct a regular polygon with an extremely large number of sides (in fact you cannot really do this either for the same reason as for the circle, but we have to idealize somewhere in order to do math). Taking the ratio of the perimeter of this polygon (which is your 44 cm) and the distance from the center to one of the vertices results in a rational approximation of $2pi$. Or, if you think from the point of view of math approximating physics rather than the other way around, $2pi$ is an approximation for these rational numbers.
In any case you've stumbled into the interesting fact that we can never really see an irrational number falling out of a physical measurement.
(As an aside, the meter isn't defined by an artifact, but rather through the definition of the second and a prespecified value for the speed of light in vacuum as measured in meters per second. This has been the case for several decades.)
answered Nov 26 at 18:04
Ian
67.3k25285
thanks for your answer. It very much cleared my doubt with such a simple explanation. I really appreciate your writing. Thanks again!
– jayant98
Nov 26 at 18:15
add a comment |
up vote
1
down vote
A circle made of a material probably cannot exist, due to small scale physical issues that are mostly off topic here. Instead, in a semi-idealized way, you can imagine that you can really construct a regular polygon with an extremely large number of sides (in fact you cannot really do this either for the same reason as for the circle, but we have to idealize somewhere in order to do math). Taking the ratio of the perimeter of this polygon (which is your 44 cm) and the distance from the center to one of the vertices results in a rational approximation of $2pi$. Or, if you think from the point of view of math approximating physics rather than the other way around, $2pi$ is an approximation for these rational numbers.
In any case you've stumbled into the interesting fact that we can never really see an irrational number falling out of a physical measurement.
(As an aside, the meter isn't defined by an artifact, but rather through the definition of the second and a prespecified value for the speed of light in vacuum as measured in meters per second. This has been the case for several decades.)
answered Nov 26 at 18:04
Ian
67.3k25285
thanks for your answer. It very much cleared my doubt with such a simple explanation. I really appreciate your writing. Thanks again!
– jayant98
Nov 26 at 18:15
add a comment |
up vote
1
down vote
up vote
1
down vote
A circle made of a material probably cannot exist, due to small scale physical issues that are mostly off topic here. Instead, in a semi-idealized way, you can imagine that you can really construct a regular polygon with an extremely large number of sides (in fact you cannot really do this either for the same reason as for the circle, but we have to idealize somewhere in order to do math). Taking the ratio of the perimeter of this polygon (which is your 44 cm) and the distance from the center to one of the vertices results in a rational approximation of $2pi$. Or, if you think from the point of view of math approximating physics rather than the other way around, $2pi$ is an approximation for these rational numbers.
In any case you've stumbled into the interesting fact that we can never really see an irrational number falling out of a physical measurement.
(As an aside, the meter isn't defined by an artifact, but rather through the definition of the second and a prespecified value for the speed of light in vacuum as measured in meters per second. This has been the case for several decades.)
answered Nov 26 at 18:04
Ian
67.3k25285
A circle made of a material probably cannot exist, due to small scale physical issues that are mostly off topic here. Instead, in a semi-idealized way, you can imagine that you can really construct a regular polygon with an extremely large number of sides (in fact you cannot really do this either for the same reason as for the circle, but we have to idealize somewhere in order to do math). Taking the ratio of the perimeter of this polygon (which is your 44 cm) and the distance from the center to one of the vertices results in a rational approximation of $2pi$. Or, if you think from the point of view of math approximating physics rather than the other way around, $2pi$ is an approximation for these rational numbers.
In any case you've stumbled into the interesting fact that we can never really see an irrational number falling out of a physical measurement.
(As an aside, the meter isn't defined by an artifact, but rather through the definition of the second and a prespecified value for the speed of light in vacuum as measured in meters per second. This has been the case for several decades.)
answered Nov 26 at 18:04
Ian
67.3k25285
answered Nov 26 at 18:04
Ian
67.3k25285
answered Nov 26 at 18:04
Ian
67.3k25285
answered Nov 26 at 18:04
Ian
67.3k25285
67.3k25285
thanks for your answer. It very much cleared my doubt with such a simple explanation. I really appreciate your writing. Thanks again!
– jayant98
Nov 26 at 18:15
add a comment |
thanks for your answer. It very much cleared my doubt with such a simple explanation. I really appreciate your writing. Thanks again!
– jayant98
Nov 26 at 18:15
thanks for your answer. It very much cleared my doubt with such a simple explanation. I really appreciate your writing. Thanks again!
– jayant98
Nov 26 at 18:15
thanks for your answer. It very much cleared my doubt with such a simple explanation. I really appreciate your writing. Thanks again!
– jayant98
Nov 26 at 18:15
add a comment |
up vote
0
down vote
I think because the 44cm long thread is the radius of the circle. This is usually rational because you don't need $π$ in the measurement of the radius in a circle.
answered Nov 26 at 18:07
LukeyBear
33
2
In an idealized situation, if you wrapped a 44 cm long straight piece of thread into a circle shape, its perimeter would be 44 cm.
– Ian
Nov 26 at 18:13
add a comment |
up vote
0
down vote
I think because the 44cm long thread is the radius of the circle. This is usually rational because you don't need $π$ in the measurement of the radius in a circle.
answered Nov 26 at 18:07
LukeyBear
33
2
In an idealized situation, if you wrapped a 44 cm long straight piece of thread into a circle shape, its perimeter would be 44 cm.
– Ian
Nov 26 at 18:13
add a comment |
up vote
0
down vote
up vote
0
down vote
I think because the 44cm long thread is the radius of the circle. This is usually rational because you don't need $π$ in the measurement of the radius in a circle.
answered Nov 26 at 18:07
LukeyBear
33
I think because the 44cm long thread is the radius of the circle. This is usually rational because you don't need $π$ in the measurement of the radius in a circle.
answered Nov 26 at 18:07
LukeyBear
33
answered Nov 26 at 18:07
LukeyBear
33
answered Nov 26 at 18:07
LukeyBear
33
answered Nov 26 at 18:07
LukeyBear
33
33
2
In an idealized situation, if you wrapped a 44 cm long straight piece of thread into a circle shape, its perimeter would be 44 cm.
– Ian
Nov 26 at 18:13
add a comment |
2
In an idealized situation, if you wrapped a 44 cm long straight piece of thread into a circle shape, its perimeter would be 44 cm.
– Ian
Nov 26 at 18:13
2
2
In an idealized situation, if you wrapped a 44 cm long straight piece of thread into a circle shape, its perimeter would be 44 cm.
– Ian
Nov 26 at 18:13
In an idealized situation, if you wrapped a 44 cm long straight piece of thread into a circle shape, its perimeter would be 44 cm.
– Ian
Nov 26 at 18:13
add a comment |
I'd say you don't have enough measurement precision to answer the question.
– Adrian Keister
Nov 26 at 18:00
3
If the circumference of a circle is $44$, then its radius is $22/pi$.
– Berci
Nov 26 at 18:01
What does that mean? Please explain...
– jayant98
Nov 26 at 18:02
1
Physical measurements have little concern about rational vs. irrational - most are precise only to 10 decimal places or thereabouts.
– Hagen von Eitzen
Nov 26 at 18:02
1
A physical thread is not a mathematical line or circle: it is a complicated three-dimensional object. Look at it under a microscope and you'll see the complications. To say that it has a certain length, and that it preserves that length when you move it, is only an approximation.
– Robert Israel
Nov 26 at 18:08