Teragon

As a monster curve or teragon ( from Greek: teras = dragon, monster), the mathematician of the late 19th and early 20th century referred to the geometric curves with highly strange properties, which were then discovered.

Examples

Examples of Monster curves are:

  • The Koch curve, introduced in 1904, is everywhere continuous but nowhere differentiable.
  • The Hilbert curve and the Peano curve composed entirely of one-dimensional lines, however, fill a two-dimensional surface. They are therefore referred to as space-filling curves.

Construction

The Monster curves are mainly due to repeated geometric rewriting systems: An initial route, called the initiator, also generator is another geometric figure called replaced. In the resulting new routes can be considered as initiators and replaced by generators now again, and this process leads if you repeat it endlessly, to curves with the aforementioned strange properties.

Many of these curves can be generated by Lindenmayer systems.

Importance

Since the mathematicians these properties appeared so strange, banished to these curves in the realm of mathematical curiosities and dealt not with them. Only gradually dealt you a closer look at the issues they raised, about the problem of dimensions. These questions often led to significant advances in mathematics.

Most monster curves are fractals.

  • Fractal geometry
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