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A method for predicting the onset of widespread chaos. It is based on the hypothesis that the dissolution of an invariant torus can be associated with the sudden change from ...

A number t_x=tan^(-1)(1/x)=cot^(-1)x, where x is an integer or rational number, tan^(-1)x is the inverse tangent, and cot^(-1)x is the inverse cotangent. Gregory numbers ...

When a point P moves along a line through the circumcenter of a given triangle Delta, the pedal circle of P with respect to Delta passes through a fixed point (the Griffiths ...

Grimm conjectured that if n+1, n+2, ..., n+k are all composite numbers, then there are distinct primes p_(i_j) such that p_(i_j)|(n+j) for 1<=j<=k.

A formula satisfied by all Hamiltonian cycles with n nodes. Let f_j be the number of regions inside the circuit with j sides, and let g_j be the number of regions outside the ...

An approach for the calculation of a Gröbner basis into several smaller computations following a path in the Gröbner fan of the ideal generated by the system of inequalities.

A honeycomb-like packing that forms hexagons.

Given n circles and a perimeter p, the total area of the convex hull is A_(Convex Hull)=2sqrt(3)(n-1)+p(1-1/2sqrt(3))+pi(sqrt(3)-1). Furthermore, the actual area equals this ...

A dozen dozen, or the square number 144.

Let E and F be paired spaces with S a family of absolutely convex bounded sets of F such that the sets of S generate F and, if B_1,B_2 in S, then there exists a B_3 in S such ...