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The depth of a vertex v in a rooted tree as the number of edges from v to the root vertex. A function to return the depth of a vertex v in a tree g may be implemented in a ...

The vertex height of a vertex v in a rooted tree is the number of edges on the longest downward path between v and a tree leaf. The height of the root vertex of a rooted tree ...

An Euler brick is a cuboid that possesses integer edges a>b>c and face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2). (3) If the ...

A regularly spaced array of points in a square array, i.e., points with coordinates (m,n,...), where m, n, ... are integers. Such an array is often called a grid or mesh, and ...

The Kummer surfaces are a family of quartic surfaces given by the algebraic equation (x^2+y^2+z^2-mu^2w^2)^2-lambdapqrs=0, (1) where lambda=(3mu^2-1)/(3-mu^2), (2) p, q, r, ...

The standard Lorentzian inner product on R^4 is given by -dx_0^2+dx_1^2+dx_2^2+dx_3^2, (1) i.e., for vectors v=(v_0,v_1,v_2,v_3) and w=(w_0,w_1,w_2,w_3), ...

In the mice problem, also called the beetle problem, n mice start at the corners of a regular n-gon of unit side length, each heading towards its closest neighboring mouse in ...

The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator ...