Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.
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Famous quotes containing the word surface:
“I have passed down the river before sunrise on a summer morning, between fields of lilies still shut in sleep; and when, at length, the flakes of sunlight from over the bank fell on the surface of the water, whole fields of white blossoms seemed to flash open before me, as I floated along, like the unfolding of a banner, so sensible is this flower to the influence of the sun’s rays.”
—Henry David Thoreau (1817–1862)
“When we are in love, the sentiment is too great to be contained whole within us; it radiates out to our beloved, finds in her a surface which stops it, forces it to return to its point of departure, and it is this rebound of our own tenderness which we call the other’s affection and which charms us more than when it first went out because we do not see that it comes from us.”
—Marcel Proust (1871–1922)
“Nature centres into balls,
And her proud ephemerals,
Fast to surface and outside,
Scan the profile of the sphere;
Knew they what that signified,
A new genesis were here.”
—Ralph Waldo Emerson (1803–1882)