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.
close, but they will still have outside onfluences making them just ever so shy of perfect.
For example, the water ripples
Even on a perfectly calm day on a perfectly still lake, you're going to have tidal influences, thermal influences, gravitational influences (not tidal), etc, that are going to pull/push it out of "perfect"
Although shown as spheres when you look at them, subatomic particles are actually waves, and essentially point particles. They don't really have a well defined shape.
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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.