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Topic: How many Rational points in graph paper can a circle have? Conjecture
then theorem

Replies: 10   Last Post: Jun 14, 2017 9:06 PM

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Wally W.

Posts: 283
Registered: 6/15/11
Re: How many Rational points in graph paper can a circle have? Conjecture then theorem
Posted: Jun 6, 2017 8:15 AM
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On Tue, 6 Jun 2017 03:29:08 -0700 (PDT), Archimedes Plutonium wrote:

>Alright the advancement on polygons makes my appetite more more. This time the circle.
>Experiment:: get out a sheet of graph paper and compass. Place the center of a large circle on a intersection point-- a Rational number point and a second rational point as radius, draw the circle and as best you can eyeball and count how many Rational number point in your circle. I counted 12. Four from a square, eight from two rectangles.
>Now i suspect the radius size has a role, dependent on the size of unit square, once past that determinant the Rational number intersects should be a constant number. I suspect the constant is 12.
>So, we have a brand new conjecture to play with.
>And the great importance of this would be to say that all circles are fully described by no more than 12 points in the plane and all circles have no more than 12 rational points and all other points of a circle are irrationals.

See discussions about lattice points here:
Pi hiding in prime regularities

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