Solving the Quintic by Iteration [PDF]
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http://math.dartmouth.edu/~doyle/docs/icos/icos.pdf  


Peter Doyle, Curt McMullen  
This paper, which appeared in Acta Mathematica, gives explicitly a new solution to the quintic polynomial, in which the transcendental inversion of the icosahedral map (due to Hermite and Kronecker) is replaced by a purely iterative algorithm. The algorithm requires a rational map with icosahedral symmetries; this paper shows that all rational maps with given symmetries can be described using the classical theory of invariant polynomials. With a historical illustration. A PostScript file and MACSYMA input and output are available from Doyle's site.  


Levels:  College, Research 
Languages:  English 
Resource Types:  Articles 
Math Topics:  Analysis, Algorithms, Differential Geometry, Symmetry/Tessellations, History and Biography 
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