In geometry, the Fermat cubic, named after Pierre de Fermat, is a surface defined by
Methods of algebraic geometry provide the following parametrization of Fermat's cubic:
In projective space the Fermat cubic is given by
The 27 lines lying on the Fermat cubic are easy to describe explicitly: they are the 9 lines of the form (w : aw : y : by) where a and b are fixed numbers with cube −1, and their 18 conjugates under permutations of coordinates.
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- Real points of Fermat cubic surface.
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Famous quotes containing the word cubic:
“Mining today is an affair of mathematics, of finance, of the latest in engineering skill. Cautious men behind polished desks in San Francisco figure out in advance the amount of metal to a cubic yard, the number of yards washed a day, the cost of each operation. They have no need of grubstakes.”
—Merle Colby, U.S. public relief program (1935-1943)