In topology, Costa's minimal surface is an embedded minimal surface and was discovered in 1982 by the Brazilianmathematician Celso Costa. It is also a surface of finite topology, which means that it has no boundaries and does not intersect itself. Its topology is a three punctured torus. A Möbius strip, a surface with only one side and one edge; such shapes are an object of study in topology. ... Verrill Minimal Surface In mathematics, a minimal surface is a surface with a mean curvature of zero. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... A torus. ...
Until its discovery, only the plane, helicoid and the catenoid were believed to be embedded surfaces that could be formed by puncturing a compact surface. The Costa surface evolves from a torus, which is deformed until the planar end becomes catenoidal. Defining these surfaces on rectangular tori of arbitary dimensions yields the Costa surface. Its discovery triggered research and discovery into several new surfaces and open conjectures in topology. Look up plane in Wiktionary, the free dictionary. ... The helicoid is one of the first minimal surfaces discovered. ... A catenoid A catenoid is a three-dimensional shape made by rotating a catenary curve around the x axis. ... In mathematics, a conjecture is a mathematical statement which has been proposed as a true statement, but which no one has yet been able to prove or disprove. ...
The Costa surface can be described using the Weierstrass zeta and the Weierstrass ellipticfunctions. In mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function called pe. Weierstrass sigma function The Weierstrass sigma function is defined as the product where denotes and is the two-dimensional lattice. ... In mathematics, Weierstrass introduced some particular elliptic functions that have become the basis for the most standard notations used. ... Partial plot of a function f. ...
References
Costa, Celso (1982). Inmersos minimas completas em R^3 de gênero um e curvatura total finita. Ph.D. Thesis, IMPA, Rio de Janeiro, Brazil.
Costa, Celso (1984). Example of a complete minimal immersion in R^3 of genus one and three embedded ends. Bol. Soc. Bras. Mat. 15, 47–54.
2006 (MMVI) is a common year starting on Sunday of the Gregorian calendar. ... November 19 is the 323rd day of the year (324th in leap years) in the Gregorian Calendar. ...
Feeds |
Contact