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Gauge theory studies principal bundle connections, called gauge fields, on a principal bundle. These connections correspond to fields, in physics, such as an electromagnetic ...

A hexagon tiling is a tiling of the plane by identical hexagons. The regular hexagon forms a regular tessellation, also called a hexagonal grid, illustrated above. There are ...

The moment of inertia with respect to a given axis of a solid body with density rho(r) is defined by the volume integral I=intrho(r)r__|_^2dV, (1) where r__|_ is the ...

The operation of exchanging all points of a mathematical object with their mirror images (i.e., reflections in a mirror). Objects that do not change handedness under ...

A polyhedron is said to be regular if its faces and vertex figures are regular (not necessarily convex) polygons (Coxeter 1973, p. 16). Using this definition, there are a ...

The turning of an object or coordinate system by an angle about a fixed point. A rotation is an orientation-preserving orthogonal transformation. Euler's rotation theorem ...

The space groups in two dimensions are called wallpaper groups. In three dimensions, the space groups are the symmetry groups possible in a crystal lattice with the ...

The trapezo-rhombic dodecahedron, also called the rhombo-trapezoidal dodecahedron, is a general dodecahedron consisting of six identical rhombi and six identical isosceles ...

There are a number of algebraic equations known as the icosahedral equation, all of which derive from the projective geometry of the icosahedron. Consider an icosahedron ...

The beautiful arrangement of leaves in some plants, called phyllotaxis, obeys a number of subtle mathematical relationships. For instance, the florets in the head of a ...