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The (circular) helicoid is the minimal surface having a (circular) helix as its boundary. It is the only ruled minimal surface other than the plane (Catalan 1842, do Carmo ...

An alternating knot is a knot which possesses a knot diagram in which crossings alternate between under- and overpasses. Not all knot diagrams of alternating knots need be ...

An n-polyhedral graph (sometimes called a c-net) is a 3-connected simple planar graph on n nodes. Every convex polyhedron can be represented in the plane or on the surface of ...

If r is a root of the polynomial equation x^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, where the a_is are integers and r satisfies no similar equation of degree <n, then r is called an ...

Many authors (e.g., Mendelson 1963; Pervin 1964) use the term arcwise-connected as a synonym for pathwise-connected. Other authors (e.g., Armstrong 1983; Cullen 1968; and ...

A paradox mentioned in the Greek work Mechanica, dubiously attributed to Aristotle. Consider the above diagram depicting a wheel consisting of two concentric circles of ...

From the point of view of coordinate charts, the notion of tangent space is quite simple. The tangent space consists of all directions, or velocities, a particle can take. In ...

The complex plane is the plane of complex numbers spanned by the vectors 1 and i, where i is the imaginary number. Every complex number corresponds to a unique point in the ...

An m-gonal n-cone graph, also called the n-point suspension of C_m or generalized wheel graph (Buckley and Harary 1988), is defined by the graph join C_m+K^__n, where C_m is ...

The distance polynomial is the characteristic polynomial of the graph distance matrix. The following table summarizes distance polynomials for some common classes of graphs. ...