Every positive integer can be written as the sum of this many perfect   squares.
After rotation and re ection, there are this many triabolos and pentiamonds. Sylvester's problem of this many points asks the probability that this many randomly chosen points in a planar region are all located on the boundary of their convex hull. The di erential equation named for phi and this number is expressed as utt − uxx + u + u3 = 0. A closed embedded smooth curve in the plane has at least this many extrema of curvature. Every positive integer can be written as the sum of this many perfect   squares. In special relativity, vectors with this many dimensions are acted upon by Lorenz transformations. For ten points, identify this number, the largest number of colors required to color a map in the plane.
After rotation and re ection, there are this many triabolos and pentiamonds.
4