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The figure eight knot, also known as the Flemish knot and savoy knot, is the unique prime knot of four crossings 04-001. It has braid word ...

A non-Euclidean space with constant negative Gaussian curvature.

The gear curve is a curve resembling a gear with n teeth given by the parametric equations x = rcost (1) y = rsint, (2) where r=a+1/btanh[bsin(nt)], (3) where tanhx is the ...

Given an original knot K, the knots produced by mutations together with K itself are called mutant knots. Mutant knots are often difficult to distinguish. For instance, ...

In three dimensions, there are three classes of constant curvature geometries. All are based on the first four of Euclid's postulates, but each uses its own version of the ...

A fixed point of a linear transformation for which the rescaled variables satisfy (delta-alpha)^2+4betagamma=0.

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called parabolic if the matrix Z=[A B; B C] (2) ...

A point p on a regular surface M in R^3 is said to be parabolic if the Gaussian curvature K(p)=0 but S(p)!=0 (where S is the shape operator), or equivalently, exactly one of ...

A metric defined by d(z,w)=sup{|ln[(u(z))/(u(w))]|:u in H^+}, where H^+ denotes the positive harmonic functions on a domain. The part metric is invariant under conformal maps ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...