View source for Teragon

{{Short description|Polygon with an infinite number of sides}}
{{distinguish|Tarragon}}
{{No inline citations|date=September 2019}}
[[File:KochFlake.svg|thumb|right|Creating a teragon, the Koch snowflake]]
[[File:Horned triangle or teragonic triangle.gif|thumb|Horned triangle or teragonic triangle]]
[[File:Karperienflake.gif|thumb|<ref>Albeverio, Sergio; Andrey, Sergio; Giordano, Paolo; and Vancheri, Alberto (1997). ''The Dynamics of Complex Urban Systems'', p.222. Springer. {{ISBN|9783790819373}}.</ref> Quadratic Koch island/Minkowski fractal]]

A '''teragon''' is a [[polygon]] with an infinite number of sides,<!--IT'S NOT FROM THE SI PREFIX--> the most famous example being the [[Koch snowflake]] ("triadic Koch teragon").{{dubious|reason=The Koch snowflake is not a polygon at all. It does not have any sides (nonzero-length line segments) in its boundary.|date=January 2022}} The term was coined by [[Benoît Mandelbrot]] from the words  [[Classical Greek]] {{lang|grc|τέρας}} (''teras'', monster) + {{lang|grc|γωνία}} (''gōnía'', corner).<ref>Larson, Ron; Hostetler, Robert P.; and Edwards, Bruce H. (1998). ''[https://books.google.com/books?id=ItFaAAAAYAAJ&q=%22teragon%22 Calculus]'', p.546. 6th edition. Houghton Mifflin. {{ISBN|9780395869741}}.</ref> 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.

==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 [[dissection (geometry)|dissected]] into smaller copies of itself.

==References==
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==Further reading==
* [[Benoit Mandelbrot|Mandelbrot, B. B.]] (1982). ''The Fractal Geometry of Nature''. W.H. Freeman and Company. {{isbn|0-7167-1186-9}}.


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[[Category:Fractals]]

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