Dividing the plane

Task number: 3320


  • Variant

    Prove that \(n\) lines can divide the plane into at most \(1+\frac{1}{2}(n^2+n)\) regions.

  • Variant

    Try to derive a similar upper bound for dividing three-dimensional space by a number of planes.

Difficulty level: Easy task (using definitions and simple reasoning)
Proving or derivation task
Cs translation
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