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 second day of July 1776, will be the most memorable epoch in the history of America. I am apt to believe that it will be celebrated by succeeding generations as the great anniversary festival. It ought to be commemorated, as the day of deliverance, by solemn acts of devotion to God Almighty. It ought to be solemnized with pomp and parade, with shows, games, sports, guns, bells, bonfires and illuminations, from one end of this continent to the other, from this time forward forever more”
—John Adams (17351826)
“It is my conviction that women are the natural orators of the race.”
—Eliza Archard Connor, U.S. suffragist. As quoted in History of Woman Suffrage, vol. 4, ch. 9, by Susan B. Anthony and Ida Husted Harper (1902)
“I saw the Arab map.
It resembled a mare shuffling on,
dragging its history like saddlebags,
nearing its tomb and the pitch of hell.”
—Adonis [Ali Ahmed Said] (b. 1930)