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A group that coincides with its commutator subgroup. If G is a non-Abelian group, its commutator subgroup is a normal subgroup other than the trivial group. It follows that ...

The perpendicular bisector of a line segment is the locus of all points that are equidistant from its endpoints. This theorem can be applied to determine the center of a ...

A planted tree is a rooted tree whose root vertex has vertex degree 1. The number of planted trees of n nodes is T_(n-1), where T_(n-1) is the number of rooted trees of n-1 ...

A point group is a group of symmetry operations which all leave at least one point unmoved. Although an isolated object may have an arbitrary Schönflies symbol, the ...

A second-order partial differential equation arising in physics, del ^2psi=-4pirho. If rho=0, it reduces to Laplace's equation. It is also related to the Helmholtz ...

A regular polygram {n/k} is generalization of a (regular) polygon on n sides (i.e., an n-gon) obtained by connecting every ith vertex around a circle with every (i+k)th, ...

The geometric centroid of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as x^_ = ...

In its simplest form, the principle of permanence states that, given any analytic function f(z) defined on an open (and connected) set U of the complex numbers C, and a ...

The Latin prefix quadri- is used to indicate the number 4, for example, quadrilateral, quadrant, etc. However, it also very commonly used to denote objects involving the ...

A quartic nonhamiltonian graph is a quartic graph that is nonhamiltonian. A number of such graphs are illustrated above. Van Cleemput and Zamfirescu (2018) gave a 39-vertex ...