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:
“It’s nice to be a part of history but people should get it right. I may not be perfect, but I’m bloody close.”
—John Lydon (formerly Johnny Rotten)
“Those who weep for the happy periods which they encounter in history acknowledge what they want; not the alleviation but the silencing of misery.”
—Albert Camus (1913–1960)
“The history of progress is written in the blood of men and women who have dared to espouse an unpopular cause, as, for instance, the black man’s right to his body, or woman’s right to her soul.”
—Emma Goldman (1869–1940)