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.
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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)
“Envy and jealousy are the private parts of the human soul. Perhaps the comparison can be extended.”
—Friedrich Nietzsche (1844–1900)
“Footnotes are the finer-suckered surfaces that allow tentacular paragraphs to hold fast to the wider reality of the library.”
—Nicholson Baker (b. 1957)