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How many times can a shape be completely surrounded by copies of itself without being able to tile the entire plane, i.e., what is the maximum (finite) Heesch number?

The Labs septic is a septic surface having 99 ordinary double points, which is the maximum number known for any septic surface.

A maximal sum-free set is a set {a_1,a_2,...,a_n} of distinct natural numbers such that a maximum l of them satisfy a_(i_j)+a_(i_k)!=a_m, for 1<=j<k<=l, 1<=m<=n.

The approximating polynomial which has the smallest maximum deviation from the true function. It is closely approximated by the Chebyshev polynomials of the first kind.

The placement of n points on a sphere so as to minimize the maximum distance of any point on the sphere from the closest one of the n points.

Possessing a single unique mode. The term unimodal distribution, which refers to a distribution having a single local maximum is a slight corruption of this definition.

Starting with a triangle, draw a circle touching two sides. Then draw a circle tangent to this circle and two other sides. Continue in the same direction. The result is a ...

The Lorentzian function is the singly peaked function given by L(x)=1/pi(1/2Gamma)/((x-x_0)^2+(1/2Gamma)^2), (1) where x_0 is the center and Gamma is a parameter specifying ...

If a function phi:(0,infty)->(0,infty) satisfies 1. ln[phi(x)] is convex, 2. phi(x+1)=xphi(x) for all x>0, and 3. phi(1)=1, then phi(x) is the gamma function Gamma(x). ...

The number of "prime" boxes is always finite, where a set of boxes is prime if it cannot be built up from one or more given configurations of boxes.