Lattice Circles

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Any three noncollinear lattice points define a circle, which can be translated and (if necessary) reflected and/or rotated so that its center lies in the triangle , , . Various lattice circles passing through four or more lattice points are precalculated for this Demonstration. For each center, the smallest lattice circle was selected that fits in a 60×60 grid and goes through exactly points.


In the lattice display, coordinates for red lattice points can be seen by hovering over them with your mouse.

In the circle centers display, the circle itself is shown, scaled down by 100.


Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA



For lattice circles going through exactly points, the results below are minimal.

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