Homogeneous Coordinate System
A point in the plane may be represented in homogeneous coordinates by a triple (x, y, z) where x/z and y/z are the Cartesian coordinates of the point. This introduces an "extra" coordinate since only two are needed to specify a point on the plane, but this system is useful in that it represents any point on the projective plane without the use of infinity. In general, a homogeneous coordinate system is one where only the ratios of the coordinates are significant and not the actual values.
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Famous quotes containing the words homogeneous and/or system:
“If we Americans are to survive it will have to be because we choose and elect and defend to be first of all Americans; to present to the world one homogeneous and unbroken front, whether of white Americans or black ones or purple or blue or green.... If we in America have reached that point in our desperate culture when we must murder children, no matter for what reason or what color, we don’t deserve to survive, and probably won’t.”
—William Faulkner (1897–1962)
“The truth is, the whole administration under Roosevelt was demoralized by the system of dealing directly with subordinates. It was obviated in the State Department and the War Department under [Secretary of State Elihu] Root and me [Taft was the Secretary of War], because we simply ignored the interference and went on as we chose.... The subordinates gained nothing by his assumption of authority, but it was not so in the other departments.”
—William Howard Taft (1857–1930)