Comparison To Surfaces
This relationship between a local invariant, the curvature, and a global topological invariant, the index, is characteristic of results in higher-dimensional Riemannian geometry such as the Gauss–Bonnet theorem.
Read more about this topic: Total Curvature
Famous quotes containing the words comparison to, comparison and/or surfaces:
“In comparison to the French Revolution, the American Revolution has come to seem a parochial and rather dull event. This, despite the fact that the American Revolution was successful—realizing the purposes of the revolutionaries and establishing a durable political regime—while the French Revolution was a resounding failure, devouring its own children and leading to an imperial despotism, followed by an eventual restoration of the monarchy.”
—Irving Kristol (b. 1920)
“Most parents aren’t even aware of how often they compare their children. . . . Comparisons carry the suggestion that specific conditions exist for parental love and acceptance. Thus, even when one child comes out on top in a comparison she is left feeling uneasy about the tenuousness of her position and the possibility of faring less well in the next comparison.”
—Marianne E. Neifert (20th century)
“Footnotes are the finer-suckered surfaces that allow tentacular paragraphs to hold fast to the wider reality of the library.”
—Nicholson Baker (b. 1957)