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Some more proofs from the Book: solvabil...

Skopenkov, A....

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Some more proofs from the Book: solvability and insolvability of equations in radicals by Skopenkov, A. ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	01-08-2023
Summary	This paper is purely expository. We present short elementary proofs of * the Gauss Theorem on constructibility of regular polygons; * the existence of a cubic equation unsolvable in real radicals; * the existence of a quintic equation unsolvable in complex radicals (Galois Theorem). The statements of these celebrated results are simple and well-known. However, their proofs given in most textbooks rely upon much unmotivated material and are far from being economic. We do not use the terms `Galois group' or even `group'. The paper is accessible for students familiar with polynomials and complex numbers, and could be an interesting easy reading for professional mathematicians. Short English version is followed by an extended Russian version where before presenting the proofs we illustrate the main ideas by sequences of problems with hints or solutions.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/0804.4357

Citation

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AMA 11th EditionReferences

Skopenkov, A.. Some more proofs from the Book: solvability and insolvability of equations in radicals. Australian National University. August 01, 2023. Accessed November 01, 2024. https://online.provdatabase.com/cite/2191

APA 7th EditionReferences

Skopenkov, A.. (2023). Some more proofs from the Book: solvability and insolvability of equations in radicals. Australian National University. https://online.provdatabase.com/cite/2191

Chicago 17th EditionReferences

Skopenkov, A.. Some more proofs from the Book: solvability and insolvability of equations in radicals. Australian National University. 2023. https://online.provdatabase.com/cite/2191

HarvardReferences

Skopenkov, A.. (2023). Some more proofs from the Book: solvability and insolvability of equations in radicals. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/2191. (Accessed 01 November 2024).

Harvard AustraliaReferences

Skopenkov, A., 2023, Some more proofs from the Book: solvability and insolvability of equations in radicals, Australian National University, viewed 01 November 2024, <https://online.provdatabase.com/cite/2191>

MLA 9th EditionWorks Cited

Skopenkov, A.. Some more proofs from the Book: solvability and insolvability of equations in radicals. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/2191.

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