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In algebraic topology, the Reidemeister torsion is a notion originally introduced as a topological invariant of 3-manifolds which has now been widely adapted to a variety of ...

Pre-Calculus

The Kähler potential is a real-valued function f on a Kähler manifold for which the Kähler form omega can be written as omega=ipartialpartial^_f. Here, the operators ...

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

Betti numbers are topological objects which were proved to be invariants by Poincaré, and used by him to extend the polyhedral formula to higher dimensional spaces. ...

An Euler brick is a cuboid that possesses integer edges a>b>c and face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2). (3) If the ...

The homotopy groups generalize the fundamental group to maps from higher dimensional spheres, instead of from the circle. The nth homotopy group of a topological space X is ...

A random walk is a sequence of discrete steps in which each step is randomly taken subject to some set of restrictions in allowed directions and step lengths. Random walks ...

Zeno's paradoxes are a set of four paradoxes dealing with counterintuitive aspects of continuous space and time. 1. Dichotomy paradox: Before an object can travel a given ...

Analysis