# Can we ever construct a perfect circle? (Curiousity)

## Homework Statement

As stated abv.

Since $$\pi$$ can only be established by infinite sum and according to zeno's paradox we can never break a finite length into infinite pieces (loosely speaking)

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Depends on your definition of perfect. It's like getting from Point A to Point B. That paradox states we can't get from A to B because we always have to cover half the remaining distance. That's not a good excuse to tell your boss why you were late, I've found out.

Mark44
Mentor
Based on the title of your thread, no, we can't construct a perfect circle. The circle of geometry is an idealized object, every point of which is the same distance away from the center. The curve that makes up the circle is infinitessimally thin, so there's no way we can draw it.

icystrike said:
Since $\pi$ can only be established by infinite sum and according to zeno's paradox we can never break a finite length into infinite pieces (loosely speaking)[/itex]
I don't understand what this has to do with your question.
??

gb7nash
Homework Helper
Like everyone else said, it depends what you're "allowed" to do. A common construction people use is an "infinite" ruler and a compass. Basically, you start with two arbitrary points in R-2 space, say (0,0) and (1,0). The only operations you're allowed to make are circles with the center at one point and the circumference on another point, and lines through two points. Any intersections you get are considered new points.

Knowing this, it's actually been proven that you cannot construct a 7-gon with with this construction. However, it has been proven that you can construct a 17-gon! (The construction is messy as hell) But to answer your question, it just depends what operations you're allowed to make.