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A closed two-form omega on a complex manifold M which is also the negative imaginary part of a Hermitian metric h=g-iomega is called a Kähler form. In this case, M is called ...

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

Abstractly, a spatial configuration F is said to possess rotational symmetry if F remains invariant under the group C=C(F). Here, C(F) denotes the group of rotations of F and ...

A list of five properties of a topological space X expressing how rich the "population" of open sets is. More precisely, each of them tells us how tightly a closed subset can ...

A schematic diagram used in logic theory to depict collections of sets and represent their relationships. The Venn diagrams on two and three sets are illustrated above. The ...

The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" ...

There are a number of attractive polyhedron compounds of two cubes. The first (left figures) is obtained by allowing two cubes to share opposite polyhedron vertices then ...

The classic treatise in geometry written by Euclid and used as a textbook for more than 1000 years in western Europe. An Arabic version The Elements appears at the end of the ...

Given a rectangle having sides in the ratio 1:phi, the golden ratio phi is defined such that partitioning the original rectangle into a square and new rectangle results in a ...

In hexagonal close packing, layers of spheres are packed so that spheres in alternating layers overlie one another. As in cubic close packing, each sphere is surrounded by 12 ...