Is a Perfect Circle Possible Given the Limitations of Pi and Space?

[HallsofIvy]

Basically, I'm saying you need a right angle to construct a square so constructing one would produce similar error to a circle.

But if you have a plane of real numbers then circle would be harder then square

You seem to be confused about "mathematical" constructions and "real world" objects. There is NO "error" or accuracy in a mathematical square or circle. They are, by definition, exact.

 

[juan gce]

We messure in straight lines .. pi .. comes naturally to make messures of a circle .. that simple and plain .. The circle's perimeter in euclidean geometry is 2pi r

 

[Saracen Rue]

Just spit balling here, but do we know if the Higgs Boson is spherical or not? Because if it's spherical, it would have to be a perfect sphere as nothing else comprises it. That would mean it's circumference would be a perfect circle.

Please any mistakes I may have made on this matter, I don't really know much about it, the thought just occurred to me and I decided to share it.

 

[HallsofIvy]

The very concept of "shape" simply does not apply to quantum objects.

 

[aikismos]

Actually, π by definition REQUIRES the perfect circle. From dictionary.com: "Perfect: conforming absolutely to the description or definition of an ideal type."

I think the OP should first take note that the circle (whether physical or conceptual) exists independent of π. That's because π is a number (concept, idea, computation, etc.) derived from two other numbers which conceptually have exact values. Back to the poster who said that the definition of a circle as a locus of point which as an "ideal type" are equidistant! That the ratio of the circumference and diameter are such that when rendered as a non-terminating, non-repeating decimal is wholly irrelevant to the existence of the "ideal type" to begin with. From a computational perspective (disregarding the drivel from neo-Platonic mumbo-jumboists) existence of the perfect circle is actually REQUIRED for the calculation of the ratio of it's parts, and not vice versa. You simply can't have π WITHOUT a perfect circle (abstractly, conceptually, computationally, informationally, etc.). Any disagreement should invoke a gentle reminder to reread the definition of perfect listed above.

Can a circle be rendered perfectly in ambient space? That's much more interesting because it depends on your definition of space. Minkowski space CERTAINLY allows for a perfect space (gravitational field around a singularity comes to mind) because Minkowski space is a mathematical construct which even under relativistic considerations allows for the use of the conceptual concept of the circle in calculations. I think the poster who brought in the effects of the wave function of particles has the strongest claim to deny the existence of the perfect circle at the quantum level (though I'm not familiar enough with the mathematics to state with certainty no such mathematical construct exists). Since QP has not replaced (but complements) RP, you can't claim it's NOT possible in space, only not possible at the quantum scale.

As long as the circle is defined as an idea (a hard notion to escape even if 'things' can 'be' round...), then a perfect circle exists both in the mathematical discourse as well as physical discourse.