Parametrization of Boy's Surface
Boy's surface can be parametrized in several ways. One parametrization, discovered by Rob Kusner and Robert Bryant, is the following: given a complex number z whose magnitude is less than or equal to one, let
so that
where x, y, and z are the desired Cartesian coordinates of a point on the Boy's surface.
If one performs an inversion of this parametrization centered on the triple point, one obtains a complete minimal surface with three "ends" (that's how this parametrization was discovered naturally). This implies that the Bryant-Kusner parametrization of Boy's surfaces is "optimal" in the sense that it is the "least bent" immersion of a projective plane into three-space.
Read more about this topic: Boy's Surface
Famous quotes containing the words boy and/or surface:
“Thus will the fondest dream of Phallic science be realized: a pristine new planet populated entirely by little boy clones of great scientific entrepeneurs ... free to smash atoms, accelerate particles, or, if they are so moved, build pyramids—without any social relevance or human responsibility at all.”
—Barbara Ehrenreich (b. 1941)
“A novelist is, like all mortals, more fully at home on the surface of the present than in the ooze of the past.”
—Vladimir Nabokov (1899–1977)