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Category Archives: Test your intuition
(Not such a set) consider a planar set A with the following property. In every direction, the distance between the two parallel lines that touch A from both sides is the same! Must A be a circle?
Let G be a graph and u and v two vertices. (1) Let H be a random graph where every edge of G is chosen with probability ½. Let p be the probability that there is a path between u … Continue reading
Question: Let be the -dimensional cube. Turn into a torus by identifying opposite facets. What is the minumum -dimensional volume of a subset of which intersects every non-trivial cycle in . Answer: Taking to be all points in the solid … Continue reading
Let be the -dimensional cube. Turn into a torus by identifying opposite facets. What is the minumum -dimensional volume of a subset of which intersects every non-trivial cycle in .
Question: Let be the cube in centered at the origin and having -dimensional volume equal to one. What is the maximum -dimensional volume of when is a hyperplane? Can you guess the behavior of when ? Can you guess the plane which … Continue reading