littlemathquark
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- Homework Statement
- At most, into how many regions can 𝑘 convex polygons divide a plane?
- Relevant Equations
- At most, into how many regions can 𝑘 convex polygons divide a plane?
One triangle divide plane 2 region, 2 triangle divide plane at most 8 region (maximum number of intersection points+2=6+2). One quadrilateral divide plane 2 region, 2 quadrilateral divide plane at most 10 region. (maximum number of intersection points+2=8+2).
So k convex n-polygon(n-gon) can divide plane ##2nC(k,2)+2## regions, but I'm not sure. I have no proof.
So k convex n-polygon(n-gon) can divide plane ##2nC(k,2)+2## regions, but I'm not sure. I have no proof.