Catálogo de publicaciones - libros
Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra
Matthias Beck Sinai Robins
Resumen/Descripción – provisto por la editorial
No disponible.
Palabras clave – provistas por la editorial
Combinatorics; Geometry; Discrete Mathematics; Number Theory; Convex and Discrete Geometry; Computational Science and Engineering
Disponibilidad
| Institución detectada | Año de publicación | Navegá | Descargá | Solicitá |
|---|---|---|---|---|
| No detectada | 2007 | SpringerLink |
Información
Tipo de recurso:
libros
ISBN impreso
978-0-387-29139-0
ISBN electrónico
978-0-387-46112-0
Editor responsable
Springer Nature
País de edición
Reino Unido
Fecha de publicación
2007
Información sobre derechos de publicación
© Springer Science+Business Media, LLC 2007
Cobertura temática
Tabla de contenidos
Solid Angles
Matthias Beck; Sinai Robins
The natural generalization of a two-dimensional angle to higher dimensions is called a . Given a pointed cone к ⊂ ℝ, the solid angle at its apex is the proportion of space that the cone к occupies. In slightly different words, if we pick a point х ∊ ℝ “at random,” then the probability that х ∊ к is precisely the solid angle at the apex of к. Yet another view of solid angles is that they are in fact volumes of spherical polytopes: the region of intersection of a cone with a sphere. There is a theory here that parallels the Ehrhart theory of Chapters 3 and 4, but which has some genuinely new ideas.
2 - Beyond the Basics | Pp. 179-190
A Discrete Version of Green’s Theorem Using Elliptic Functions
Matthias Beck; Sinai Robins
We now allow ourselves the luxury of using basic complex analysis. In particular, we assume that the reader is familiar with contour integration and the residue theorem. We may view the residue theorem as yet another result that intimately connects the continuous and the discrete: it transforms a continuous integral into a discrete sum of residues.
2 - Beyond the Basics | Pp. 191-197