Moving Frames
The Darboux frame is an example of a natural moving frame defined on a surface. With slight modifications, the notion of a moving frame can be generalized to a hypersurface in an n-dimensional Euclidean space, or indeed any embedded submanifold. This generalization is among the many contributions of Élie Cartan to the method of moving frames.
Read more about this topic: Darboux Frame
Famous quotes containing the words moving and/or frames:
“Imagination could hardly do without metaphor, for imagination is, literally, the moving around in one’s mind of images, and such images tend commonly to be metaphoric. Creative minds, as we know, are rich in images and metaphors, and this is true in science and art alike. The difference between scientist and artist has little to do with the ways of the creative imagination; everything to do with the manner of demonstration and verification of what has been seen or imagined.”
—Robert A. Nisbet (b. 1913)
“The bird would cease and be as other birds
But that he knows in singing not to sing.
The question that he frames in all but words
Is what to make of a diminished thing.”
—Robert Frost (1874–1963)