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In other words: 1) Take a regular n-gon P. 2) Inscribe a circle C1, and circumscribe a circle C2. 3) The parts of C2 that lie outside P are n circle segments
by cousin_it 11y ago
In other words:
1) Take a regular n-gon P.
2) Inscribe a circle C1, and circumscribe a circle C2.
3) The parts of C2 that lie outside P are n circle segments, whose straight sides are tangent to C1.
4) If you move these segments around in any way, they will overlap each other, so the uncovered area of C2 will become larger.
5) Therefore P is the smallest possible n-gon whose inscribed circle is C1.
- SilasX 11y agoSo the new property found is that, for any given circle C1, the smallest n-gon whose inscribed circle is C1 is a regular n-gon? Edit: rephrasing.