History
Parameter space contributed to the liberation of geometry from the confines of three-dimensional space. For instance, the parameter space of spheres in three dimensions, has four dimensions -- three for the sphere center and another for the radius. According to Dirk Struik, it was the book Neue Geometrie des Raumes (1849) by Julius Plücker that showed
- ...geometry need not solely be based on points as basic elements. Lines, planes, circles, spheres can all be used as the elements (Raumelemente) on which a geometry can be based. This fertile conception threw new light on both synthetic and algebraic geometry and created new forms of duality. The number of dimensions of a particular form of geometry could now be any positive number, depending on the number of parameters necessary to define the "element".
The requirement for higher dimensions is illustrated by Plücker's line geometry. Struik writes
- geometry of lines in three-space could be considered as a four-dimensional geometry, or, as Klein has stressed, as the geometry of a four-dimensional quadric in a five-dimensional space.
Read more about this topic: Parameter Space
Famous quotes containing the word history:
“The history of the Victorian Age will never be written: we know too much about it.”
—Lytton Strachey (1880–1932)
“The history of the past is but one long struggle upward to equality.”
—Elizabeth Cady Stanton (1815–1902)
“The history of this country was made largely by people who wanted to be left alone. Those who could not thrive when left to themselves never felt at ease in America.”
—Eric Hoffer (1902–1983)