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The Royale", an episode (first aired 27 March 1989) of Star Trek: The Next Generation, begins with Picard attempting to solve the puzzle in his ready room; he remarks to Riker that the theorem had remained unproven for 800 years. [13] The captain ends the episode with the line "Like Fermat's theorem, it is a puzzle we may never solve."
Even after such symmetry reductions, the reduced system of equations is often difficult to solve. For example, the Ernst equation is a nonlinear partial differential equation somewhat resembling the nonlinear Schrödinger equation (NLS). But recall that the conformal group on Minkowski spacetime is the symmetry group of the Maxwell equations.
Fermat's Last Theorem considers solutions to the Fermat equation: a n + b n = c n with positive integers a, b, and c and an integer n greater than 2. There are several generalizations of the Fermat equation to more general equations that allow the exponent n to be a negative integer or rational, or to consider three different exponents.
The existence of anti-gravity is a common theme in science fiction. [45] The Encyclopedia of Science Fiction lists Francis Godwin's posthumously-published 1638 novel The Man in the Moone, where a "semi-magical" stone has the power to make gravity stronger or weaker, as the earliest variation of the theme. [45]
The word theory in "the theory of evolution" does not imply scientific doubt regarding its validity; the concepts of theory and hypothesis have specific meanings in a scientific context. While theory in colloquial usage may denote a hunch or conjecture, a scientific theory is a set of principles that explains an observable phenomenon in natural ...
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force (where the work done is independent of path), with that of the total potential energy of the system.
Science-Fiction Handbook, subtitled The Writing of Imaginative Fiction, is a guide to writing and marketing science fiction and fantasy by L. Sprague de Camp, "one of the earliest books about modern sf." [1] The original edition was published in hardcover by Hermitage House in 1953 as a volume in its Professional Writers Library series.
One of the widely used types of impossibility proof is proof by contradiction.In this type of proof, it is shown that if a proposition, such as a solution to a particular class of equations, is assumed to hold, then via deduction two mutually contradictory things can be shown to hold, such as a number being both even and odd or both negative and positive.