Usefulness
The fish curve itself may not have any known applications to physical systems, but parametric equations in general do. Using parametric equations to express curves is practical as well as efficient; for example, one can integrate and differentiate such curves termwise. In general, a parametric curve is a function of one independent parameter, which is usually represented by t, while the symbols u and v are commonly used for parametric equations in two parameters.
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Famous quotes containing the word usefulness:
“This monument, so imposing and tasteful, fittingly typifies the grand and symmetrical character of him in whose honor it has been builded. His was “the arduous greatness of things done.” No friendly hands constructed and placed for his ambition a ladder upon which he might climb. His own brave hands framed and nailed the cleats upon which he climbed to the heights of public usefulness and fame.”
—Benjamin Harrison (1833–1901)
“A public man must never forget that he loses his usefulness when he as an individual, rather than his policy, becomes the issue.”
—Richard M. Nixon (1913–1995)
“But, in history, practical usefulness never determines the moral value of an achievement. Only the person who increases the knowledge humanity has about itself and enhances its creative consciousness permanently enriches humanity.”
—Stefan Zweig (18811942)