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A fake knot (i.e., a knot equivalent to the unknot) created by tying a square knot, then looping one end twice through the knot such that when both ends are pulled, the knot ...

The 6-polyiamond illustrated above.

A node which is one graph edge further away from a given node in a rooted tree.

A chiral knot is a knot which is not capable of being continuously deformed into its own mirror image. A knot that can be so deformed is then called an amphichiral knot. ...

The locus of the point at which two given circles possess the same circle power is a straight line perpendicular to the line joining the midpoints of the circle and is known ...

sum_(k=0)^m(phi_k(x)phi_k(y))/(gamma_k)=(phi_(m+1)(x)phi_m(y)-phi_m(x)phi_(m+1)(y))/(a_mgamma_m(x-y),) (1) where phi_k(x) are orthogonal polynomials with weighting function ...

Let {p_n(x)} be orthogonal polynomials associated with the distribution dalpha(x) on the interval [a,b]. Also let rho=c(x-x_1)(x-x_2)...(x-x_l) (for c!=0) be a polynomial of ...

A Chu space is a binary relation from a set A to an antiset X which is defined as a set which transforms via converse functions.

Let a graph G have graph vertices with vertex degrees d_1<=...<=d_m. If for every i<n/2 we have either d_i>=i+1 or d_(n-i)>=n-i, then the graph is Hamiltonian.

It is possible to place 7 cigarettes in such a way that each touches every other if l/d>7sqrt(3)/2 (Gardner 1959, p. 115).