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The plane determined by the points x_1, x_2, and x_3 and the line passing through the points x_4 and x_5 intersect in a point which can be determined by solving the four ...

Any linear system of point-groups on a curve with only ordinary singularities may be cut by adjoint curves.

Two curves phi and psi satisfying phi+psi=0 are said to be linearly dependent. Similarly, n curves phi_i, i=1, ..., n are said to be linearly dependent if sum_(i=1)^nphi_i=0.

Sequences x_n^((1)), x_n^((2)), ..., x_n^((k)) are linearly dependent if constants c_1, c_2, ..., c_k (not all zero) exist such that sum_(i=1)^kc_ix_n^((i))=0 for n=0, 1, ....

The least number of crossings that occur in any projection of a link. In general, it is difficult to find the crossing number of a given link. Knots and links are generally ...

This is proven in Rademacher and Toeplitz (1957).

In space, the only conformal mappings are inversions, similarity transformations, and congruence transformations. Or, restated, every angle-preserving transformation is a ...

The lengths of the tangents from a point P to a conic C are proportional to the cube roots of the radii of curvature of C at the corresponding points of contact.

The inverse curve of the lituus is an Archimedean spiral with m=2, which is Fermat's spiral.

The local clustering coefficient of a vertex v_i of a graph G is the fraction of pairs of neighbors of v_i that are connected over all pairs of neighbors of v_i. Computation ...