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Blair Spearman and Kenneth S. Williams, "Characterization of solvable quintics x 5 + ax + b, American Mathematical Monthly, 101:986–992 (1994). Ian Stewart, Galois Theory 2nd Edition, Chapman and Hall, 1989. ISBN 0-412-34550-1. Discusses Galois Theory in general including a proof of insolvability of the general quintic.
Probability: Theory and Examples (PDF). Cambridge Series in Statistical and Probabilistic Mathematics. Vol. 49 (5th ed.). Cambridge New York, NY: Cambridge University Press. ISBN 978-1-108-47368-2. OCLC 1100115281
This does not follow from Abel's statement of the theorem, but is a corollary of his proof, as his proof is based on the fact that some polynomials in the coefficients of the equation are not the zero polynomial. This improved statement follows directly from Galois theory § A non-solvable quintic example. Galois theory implies also that
A 2-colouring of K 5 with no monochromatic K 3. The conclusion to the theorem does not hold if we replace the party of six people by a party of fewer than six. To show this, we give a coloring of K 5 with red and blue that does not contain a triangle with all edges the same color. We draw K 5 as a pentagon surrounding a star (a pentagram). We ...
For example, S 5, the symmetric group in 5 elements, is not solvable which implies that the general quintic equation cannot be solved by radicals in the way equations of lower degree can. The theory, being one of the historical roots of group theory, is still fruitfully applied to yield new results in areas such as class field theory.
In physics, Kaluza–Klein theory (KK theory) is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the common 4D of space and time and considered an important precursor to string theory. In their setup, the vacuum has the usual 3 dimensions of space and one dimension of time ...
The specific characteristics of a putative fifth force depend on which hypothesis is being advanced. No evidence to support these models has been found. The term is also used as "the Fifth force" when referring to a specific theory advanced by Ephraim Fischbach in 1971 to explain experimental deviations in the theory of gravity. Later analysis ...
The theory has been applied in various fields of engineering and management. Initially, the grey method was adapted to effectively study air pollution [ 4 ] and subsequently used to investigate the nonlinear multiple-dimensional model of the socio-economic activities’ impact on the city air pollution. [ 5 ]