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There exist polyhedra which can be plaited (braided). Examples include a plaited cube and plaited icosahedron illustrated above (Pargeter 1959, Wells 1991). In the above ...

A planar connected graph is a graph which is both planar and connected. The numbers of planar connected graphs with n=1, 2, ... nodes are 1, 1, 2, 6, 20, 99, 646, 5974, ...

A planar embedding, also called a "plane graph" (Harary 1994, p. 103; Harborth and Möller 1994), "planar drawing," or "plane drawing," of a planar graph is an embedding in ...

Flat polygons embedded in three-space can be transformed into a congruent planar polygon as follows. First, translate the starting vertex to (0, 0, 0) by subtracting it from ...

Plancherel's theorem states that the integral of the squared modulus of a function is equal to the integral of the squared modulus of its spectrum. It corresponds to ...

Planck's's radiation function is the function f(x)=(15)/(pi^4)1/(x^5(e^(1/x)-1)), (1) which is normalized so that int_0^inftyf(x)dx=1. (2) However, the function is sometimes ...

Consider n intersecting circles. The maximal number of regions into which these divide the plane are N(n)=n^2-n+2, giving values for n=1, 2, ... of 2, 4, 8, 14, 22, 32, 44, ...

A planted plane tree (V,E,v,alpha) is defined as a vertex set V, edges set E, root v, and order relation alpha on V which satisfies 1. For x,y in V if rho(x)<rho(y), then ...

A planted tree is a rooted tree whose root vertex has vertex degree 1. The number of planted trees of n nodes is T_(n-1), where T_(n-1) is the number of rooted trees of n-1 ...

The partial differential equation (1+u_y^2)u_(xx)-2u_xu_yu_(xy)+(1+u_x^2)u_(yy)=0 (correcting a typo in Zwillinger 1997, p. 134).