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On Klein’s icosahedral solution of the quintic. (English) Zbl 1319.12001

Summary: We present an exposition of the icosahedral solution of the quintic equation first described in F. Klein’s classic work [“Lectures on the icosahedron and the solution of equations of the fifth degree.” (German) Leipzig: Teubner (1884; JFM 16.0061.01)]. Although we are heavily influenced by Klein we follow a slightly different approach which enables us to arrive at the solution more directly.

MSC:

12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
13A50 Actions of groups on commutative rings; invariant theory
51M20 Polyhedra and polytopes; regular figures, division of spaces

Citations:

JFM 16.0061.01

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References:

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