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It is especially convenient to specify planes in so-called Hessian normal form. This is obtained from the general equation of a plane ax+by+cz+d=0 (1) by defining the ...

A solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series ...

A two-component complex column vector. Spinors can describe both bosons and fermions, while tensors can describe only bosons.

A portion of a disk whose upper boundary is a (circular) arc and whose lower boundary is a chord making a central angle theta<pi radians (180 degrees), illustrated above as ...

A complete k-partite graph is a k-partite graph (i.e., a set of graph vertices decomposed into k disjoint sets such that no two graph vertices within the same set are ...

The 10.1.2 equation A^(10)=B^(10)+C^(10) (1) is a special case of Fermat's last theorem with n=10, and so has no solution. No 10.1.n solutions are known with n<13. A 10.1.13 ...

The 8.1.2 equation A^8+B^8=C^8 (1) is a special case of Fermat's last theorem with n=8, and so has no solution. No 8.1.3, 8.1.4, 8.1.5, 8.1.6, or 8.1.7 solutions are known. ...

The Franklin graph is the 12-vertex cubic graph shown above whose embedding on the Klein bottle divides it into regions having a minimal coloring using six colors, thus ...

In a boarding school there are fifteen schoolgirls who always take their daily walks in rows of threes. How can it be arranged so that each schoolgirl walks in the same row ...

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. A vertex coloring that minimize ...