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)
“Clay answered the petition by declaring that while he looked on the institution of slavery as an evil, it was ‘nothing in comparison with the far greater evil which would inevitably flow from a sudden and indiscriminate emancipation.’”
—State of Indiana, U.S. public relief program (1935-1943)
“But ice-crunching and loud gum-chewing, together with drumming on tables, and whistling the same tune seventy times in succession, because they indicate an indifference on the part of the perpetrator to the rest of the world in general, are not only registered on the delicate surfaces of the brain but eat little holes in it until it finally collapses or blows up.”
—Robert Benchley (1889–1945)