Advertisement

The natural generalization of a two-dimensional angle to higher dimensions is called a solid angle. Given a pointed cone к ⊂ ℝd, 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 ∊ ℝd “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.

Keywords

Solid Angle Discrete Volume Ehrhart Polynomial Rational Convex Rational Polytopes 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media, LLC 2007

Personalised recommendations