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Results tagged with plane-geometry
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user 20186
Plane Geometry is about flat shapes like lines, circles and triangles , shapes that can be drawn on a piece of paper
4
votes
Convex curves with many inscribed triangles maximizing perimeter
This 1988 paper of Innami gives a construction of a convex curve, all of whose points are vertices of billiard triangles and therefore also maximal-perimeter inscribed triangles. In Innami's construct …
- 5,971
3
votes
Optimal stacking of split logs
I don't know if this is the optimal packing of 1/6-circle wedges, but I do know that the following is the optimal packing of the shape formed by gluing two of those wedges along a full edge:
The tw …
- 5,971
2
votes
11
votes
Accepted
2-layer tilings with a center-of-gravity constraint
The pentagon $(0,0)(0,1)(1/2,1+x)(1,1),(1,0)$ with $x=(\sqrt{21}-3)/4$ gives a double coverage fraction of $x/2=0.1978\ldots$.
UPDATE: The triangle can get you $1/8=0.125$
- 5,971