Definition, Betydelse & Synonymer | Engelska ordet QUINTIC

Definition av QUINTIC

1. kvintisk
2. (matematik) femtegradare, femtegradsekvation, femtegradspolynom

Exempel på hur man kan använda QUINTIC i en mening

• His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals.
• Historically, the word "solvable" arose from Galois theory and the proof of the general unsolvability of quintic equations.
• Iterative methods are the only ones available for quintic and higher-order equations, beyond trivial or special cases.
• Some abstract problems have been rigorously proved to be unsolvable, such as squaring the circle and trisecting the angle using only the compass and straightedge constructions of classical geometry, and solving the general quintic equation algebraically.
• Niels Henrik Abel partially proves that the general quintic or higher equations cannot be solved by a general formula involving only arithmetical operations and roots.
• Solving quintic equations in terms of radicals (nth roots) was a major problem in algebra from the 16th century, when cubic and quartic equations were solved, until the first half of the 19th century, when the impossibility of such a general solution was proved with the Abel–Ruffini theorem.
• For example, if the rational root theorem produces a single (rational) root of a quintic polynomial, it can be factored out to obtain a quartic (fourth degree) quotient; the explicit formula for the roots of a quartic polynomial can then be used to find the other four roots of the quintic.
• It is possible to solve the quintic equation if general hypergeometric functions are included, although the solution is far too complicated algebraically to be useful.
• One major use of his results is the parametrization of quartic and quintic orders in number fields, thus allowing the study of the asymptotic behavior of the arithmetic properties of these orders and fields.
• Apple uses an approximation of a squircle (actually a quintic superellipse) for icons in iOS, iPadOS, macOS, and the home buttons of some Apple hardware.
• A more restricted class of sextics can be solved by the one-variable generalised hypergeometric function using Felix Klein's approach to solving the quintic equation.
• Other common topics for crankery, collected by Dudley, include calculations for the perimeter of an ellipse, roots of quintic equations, Fermat's little theorem, Gödel's incompleteness theorems, Goldbach's conjecture, magic squares, divisibility rules, constructible polygons, twin primes, set theory, statistics, and the Van der Pol oscillator.
• In algebraic geometry, the Enriques–Babbage theorem states that a canonical curve is either a set-theoretic intersection of quadrics, or trigonal, or a plane quintic.
• In 1858, Charles Hermite, Leopold Kronecker, and Francesco Brioschi independently discovered that the quintic equation could be solved with elliptic transcendents.

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