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:
“What we call National-Socialism is the poisonous perversion of ideas which have a long history in German intellectual life.”
—Thomas Mann (1875–1955)
“The history of literature—take the net result of Tiraboshi, Warton, or Schlegel,—is a sum of a very few ideas, and of very few original tales,—all the rest being variation of these.”
—Ralph Waldo Emerson (1803–1882)
“Regarding History as the slaughter-bench at which the happiness of peoples, the wisdom of States, and the virtue of individuals have been victimized—the question involuntarily arises—to what principle, to what final aim these enormous sacrifices have been offered.”
—Georg Wilhelm Friedrich Hegel (1770–1831)