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The surface of revolution generated by the external catenary between a fixed point a and its conjugate on the envelope of the catenary through the fixed point is equal in ...

A planar diagram depicting a link (or knot) as a sequence of segments with gaps representing undercrossings and solid lines overcrossings. In such a diagram, only two ...

Eliminate each knot crossing by connecting each of the strands coming into the crossing to the adjacent strand leaving the crossing. The resulting strands no longer cross but ...

The angular twist theta of a shaft with given cross section is given by theta=(TL)/(KG) (1) (Roark 1954, p. 174), where T is the twisting moment (commonly measured in units ...

If P=p:q:r and U=u:v:w are distinct trilinear points, neither lying on a sideline of the reference triangle DeltaABC, then the crosspoint of P and U is the point ...

All closed surfaces, despite their seemingly diverse forms, are topologically equivalent to spheres with some number of handles or cross-caps. The traditional proof follows ...

If the cross ratio kappa of {AB,CD} satisfy kappa^2-kappa+1=0, (1) then the points are said to form a bivalent range, and {AB,CD}={AC,DB}={AD,BC}=kappa (2) ...

The contact angle between a sphere and a tangent plane is the angle alpha between the normal to the sphere at the point of tangency and the basal plane with respect to which ...

A quadratic recurrence is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a second-degree polynomial in x_k with k<n. For example, x_n=x_(n-1)x_(n-2) ...

A maximally nonhamiltonian graph is a nonhamiltonian graph G for which G+e is Hamiltonian for each edge e in the graph complement of G^_, i.e., every two nonadjacent vertices ...