Topology
Topology is a branch of mathematics concerned with the properties of
geometrical figures that remain unchanged when they are transformed by
bending, stretching, shrinking, or twisting. Hence, topology, unlike
classical geometry, focuses on relative positions and continuity.
Compactness, connectedness, closed curves are just some of the
properties of spaces and maps that are examined. The Konigsberg Bridge
problem and the four-color theorem are two of the most prominent
problems of topology.
Many people are introduced to topology not through its abstract
properties but through a more recreational approach. Topology is
sometimes referred to as a "rubber sheet geometry" since it involves the
deforming ideally elastic objects. Mobius bands, helixes, Klein
bottles, and knots are just some of the "mathematical toys" that can be
played with when exploring topology.
Today, there are many serious and powerful applications of topology
including DNA modeling, particle physics, and cosmology. Research
is currently being done in such areas such as network topology, digital
topology, knot theory and crystallographic topology, just to name a
few.
A brief
introduction to topology
Lesson
Plans and Topology Activities for the classroom
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