In
mathematics, the Loch Ness monster is a
surface
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...
with infinite
genus
Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial nom ...
but only one
end
End, END, Ending, or variation, may refer to:
End
*In mathematics:
** End (category theory)
** End (topology)
**End (graph theory)
** End (group theory) (a subcase of the previous)
**End (endomorphism)
*In sports and games
**End (gridiron footbal ...
. It appeared named this way already in a 1981 article by . The surface can be constructed by starting with a plane (which can be thought of as the surface of
Loch Ness
Loch Ness (; gd, Loch Nis ) is a large freshwater loch in the Scottish Highlands extending for approximately southwest of Inverness. It takes its name from the River Ness, which flows from the northern end. Loch Ness is best known for claim ...
) and adding an infinite number of handles (which can be thought of as loops of the
Loch Ness monster
The Loch Ness Monster ( gd, Uilebheist Loch Nis), affectionately known as Nessie, is a creature in Scottish folklore that is said to inhabit Loch Ness in the Scottish Highlands. It is often described as large, long-necked, and with one or mor ...
).
See also
*
Cantor tree surface
In dynamical systems, the Cantor tree is an infinite-genus surface homeomorphic to a sphere with a Cantor set removed. The blooming Cantor tree is a Cantor tree with an infinite number of handles added in such a way that every end is a limit of ha ...
*
Jacob's ladder surface
References
*
*
*
*{{Citation , last1=Arredondo , first1=John A. , last2=Ramírez-Maluendas , first2= Camilo, title=On the Infinite Loch Ness monster , url=http://cmuc.karlin.mff.cuni.cz/cmuc1704/abs/arredo.htm , doi=10.14712/1213-7243.2015.227 , year=2017 , journal= Commentationes Mathematicae Universitatis Carolinae, issn=0010-2628 , volume=58 , issue=4 , pages=465–479, arxiv=1701.07151 , bibcode=2017arXiv170107151A
Surfaces
Loch Ness Monster