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A braid index is the least number of strings needed to make a closed braid representation of a link. The braid index is equal to the least number of Seifert circles in any ...

The least number of unknotted arcs lying above the plane in any projection. The knot 05-002 has bridge number 2. Such knots are called 2-bridge knots. There is a one-to-one ...

The term "bundle" is an abbreviated form of the full term fiber bundle. Depending on context, it may mean one of the special cases of fiber bundles, such as a vector bundle ...

The Cairo tessellation is a tessellation appearing in the streets of Cairo and in many Islamic decorations. Its tiles are obtained by projection of a dodecahedron, and it is ...

The product of a family {X_i}_(i in I) of objects of a category is an object P=product_(i in I)X_i, together with a family of morphisms {p_i:P->X_i}_(i in I) such that for ...

A compactification of a topological space X is a larger space Y containing X which is also compact. The smallest compactification is the one-point compactification. For ...

A covering map (also called a covering or projection) is a surjective open map f:X->Y that is locally a homeomorphism, meaning that each point in X has a neighborhood that is ...

Let a knot K be parameterized by a vector function v(t) with t in S^1, and let w be a fixed unit vector in R^3. Count the number of local minima of the projection function ...

A cross section of a solid is a plane figure obtained by the intersection of that solid with a plane. The cross section of an object therefore represents an infinitesimal ...

Let DeltaA^'B^'C^' be a triangle perspective to a reference triangle DeltaABC with perspector D^(''). Let A^('') be the intersection of lines BC^' and CB^', B^('') the ...