Convex Hull of Grid Points in a Circle

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2013-05-24 04:36

This example demonstrates generating grid points inside a circle and computing their convex hull. Key math concepts include circle, symmetry, orthocenter, hypergeometric distribution, limits, right triangles, and rational numbers. It uses GeoGebra commands like Sequence, Flatten, ConvexHull, and Circle. Suitable for high school mathematics teaching, illustrating geometric constructions and algorithm applications.

GeoGebra Commands & Parameters

Sequence(Sequence[If[(i - x(A))^(2) + (j - y(A))^(2) ≤ r^(2), (i, j)], i, ceil(-2 * r + x(A)), floor(r + x(A))], j, ceil(-2 * r + y(A)), floor(r + y(A))) → list3
Sequence(Sequence[If[i^(2) + j^(2) ≤ r^(2), (i, j)], i, ceil(-r), floor(r)], j, ceil(-r), floor(r)) → list1
Flatten(list1) → list2
ConvexHull(list2) → graph1
Circle(A, r) → d
Flatten(list3) → list4
ConvexHull(list4) → graph2

AI Drawing Prompt Reference

Draw a circle with radius r centered at point A. Generate grid points inside the circle and compute their convex hull. Then, generate grid points in the entire coordinate system and compute their convex hull. Finally, draw both convex hulls.

The prompt above was compiled from the original drawing commands and is for reference only.