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Fixing and almost fixing a planar convex body
Augustin Fruchard
A set of points a 1 ,. .. , a n fixes a planar convex body K if the points are on bdK, the boundary of K, and if any small move of K brings some point of the set in intK, the inter…
Fair partitioning by straight lines
Augustin Fruchard, Alexander Magazinov
A pizza is a pair of planar convex bodies ,where represents the dough and the topping of the pizza. A partition of a pizza by straight lines is a succession o…
Envelopes of -sections
Nicolas Chevallier, Augustin Fruchard, Costin Vîlcu
Let be a planar convex body af area , and take $0 \textless{} α\textless{} 1$.An -section of is a line cutting into two parts, one of whichhas area . This…
Small holding circles
Augustin Fruchard
A circle C holds a convex body K if C does not meet the interior of K and if there does not exist any euclidean displacement which moves C as far as desired from K, avoiding the in…