Teragon
This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (September 2019) |
A teragon is a polygon with an infinite number of sides, the most famous example being the Koch snowflake ("triadic Koch teragon"). Typically, a teragon will be bounded by one or more self-similar fractal curves, which are created by replacing each line segment in an initial figure with multiple connected segments, then replacing each of those segments with the same pattern of segments, then repeating the process an infinite number of times for every line segment in the figure.
Etymology[]
To describe the Koch snowflake, Mandelbrot coined the term teragon, which translates literally from the Greek words for "monster curve."[2]
The word "teragon" comes from Greek τέρας (teras), "monster, marvel", + γωνία (gōnía) "corner, angle" (as in polygon). By the standards of classical geometry, a teragon like the Koch snowflake was a marvelous or monstrous object requiring new techniques to understand and analyze.
A teragon is a shape with infinite sides. It is commonly known as the Koch snowflake.
Other examples[]
The horned triangle, created by erecting a series of smaller triangles on one corner of an equilateral triangle, is another example of a teragon. It is also an example of a rep-tile, or shape that can be completely dissected into smaller copies of itself.
References[]
Further reading[]
- Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. W.H. Freeman and Company. ISBN 0-7167-1186-9.
- Fractals
- Geometry stubs