topology

Some properties of a geometric figure remain unchanged when it is distorted; for example the two lines still intersect.

The Möbius strip has only one side and one edge. It consists of a strip of paper connected at its ends with a half-twist in the middle.

The Könisberg bridge problem. The challenge is to cross each of the seven bridges (top) over the River Pregol'a in Königsberg (now Kaliningrad, Russia) once only and return to one's starting point. Representing the puzzle as a topological network (bottom) shows that this is impossible.

Branch of geometry that deals with those properties of a figure that remain unchanged even when the figure is transformed (bent, stretched) – for example, when a square painted on a rubber sheet is deformed by distorting the sheet.

Topology has scientific applications, as in the study of turbulence in flowing fluids.

The topological theory, proposed in 1880, that only four colours are required in order to produce a map in which no two adjoining countries have the same colour, inspired extensive research, and was proved in 1972 by Kenneth Appel and Wolfgang Haken.

The map of a subway system is an example of the topological representation of a network; connectivity (the way the lines join together) is preserved, but shape and size are not.

topology

In computing, the arrangement of devices in a network. The most common is the bus topology, where all the computers are interconnected using a single, open-ended cable. Most modern network solutions use either a ring or bus layout, but with physical characteristics that resemble a star layout.