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Consider a simple closed curve $C$ in $\mathbb{R}^2$. For any points $a$ and $b$ on this curve we associate a point $c_1$ on the left and $c_2$ on the right side to the chord ab, such that $ac_1bc_2$ ...

Consider a simple closed curve $C$ in $\mathbb{R}^2$. For any points $a$ and $b$ on this curve we associate point $c$ on the left (or right) side to chord $ab$ such that $\angle acb = 90^{\circ}, ac=...

8 cubes can be joined face-to-face to form a closed ring with a hole in it, with each cube sharing a face with only two others. The same can be done with 8 dodecahedrons. Is the same possible with the ...