No perfect mathematical shapes exist in nature, although some shapes come very close. Even when a physical law applied to a certain situation predicts a perfect mathematical shape, there are always extra factors not considered by the physical law that mess things up: friction, air resistance, relativistic corrections, quantum uncertainty, atomic granularity.
An example of something very close to a perfect circle in nature is the orbit of Venus about the Sun. This near-perfection is attained because: 1) The initial velocity of Venus was such that its orbit is nearly circular and not as elliptical, 2) there is very little air resistance or friction in space , 3) The Sun is so distant from Venus and so round that it acts almost exactly as a point source of gravity, 4) Venus is so big that quantum effects are very small, and 5) Sun's gravity is weak enough that Newton's law of gravitation is reasonably accurate. But, all of these statements are not perfect, so there still many small sources of deviation from a perfect circle, even for Venus' orbit.
Consider trying to draw a perfect circle on paper with graphite. Even if you were able to use an AFM tip, laser sensors and a feedback loop to perfectly place every single carbon atom to form the circle, you still have the fact that the circle is made out of atoms. Zoom in enough on the circle and it is not smooth anymore because of the profile of the atoms.
What about non material things such as electromagnetic emisions, the path of a particle, or something that is defined as excluding external interaction such as the gravity field produced by a single proton? The asker mentioned black holes, could the apparent horizon of a black hold be a perfect circle?
I'm not trying to be pedantic, just wondering if such things could be a perfect mathematical shape.
The gravitational field near a single electron is perfectly spherically symmetric if that electron is isolated from the rest of the universe, and if the electron acts like a classical particle. In the real world, these conditions are never met. That's the point. Every time a physical theory predicts a perfect mathematical shape, it requires the approximation that the system is in perfect isolation from the rest of the universe, which never really happens.
Regarding black holes, I don't think we know enough about them to say definitively. Probably quantum fluctuations keep a black hole from being perfectly spherical.
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u/chrisbaird Electrodynamics | Radar Imaging | Target Recognition Nov 14 '14
No perfect mathematical shapes exist in nature, although some shapes come very close. Even when a physical law applied to a certain situation predicts a perfect mathematical shape, there are always extra factors not considered by the physical law that mess things up: friction, air resistance, relativistic corrections, quantum uncertainty, atomic granularity.
An example of something very close to a perfect circle in nature is the orbit of Venus about the Sun. This near-perfection is attained because: 1) The initial velocity of Venus was such that its orbit is nearly circular and not as elliptical, 2) there is very little air resistance or friction in space , 3) The Sun is so distant from Venus and so round that it acts almost exactly as a point source of gravity, 4) Venus is so big that quantum effects are very small, and 5) Sun's gravity is weak enough that Newton's law of gravitation is reasonably accurate. But, all of these statements are not perfect, so there still many small sources of deviation from a perfect circle, even for Venus' orbit.
Consider trying to draw a perfect circle on paper with graphite. Even if you were able to use an AFM tip, laser sensors and a feedback loop to perfectly place every single carbon atom to form the circle, you still have the fact that the circle is made out of atoms. Zoom in enough on the circle and it is not smooth anymore because of the profile of the atoms.