Lectures on the Icosahedron (Dover Phoenix Editions): Felix Klein

Description

Product Description:
This notable work covers the solution of quintics in terms of the rotations of a regular icosahedron around the axes of its symmetry. It begins with the theory of the icosahedron itself; regular solids and theory of groups; and then explores the theory of equations of the 5th degree; introduces geometrical material, more.

Review:
This is a famous book first published in German in 1884. In a fairly elementary way Professor Klein finds algebraic equations for the tetrahedron, cube and icosahedron by means of their rotational and reflection symmetry.Unfortunately there are no Figures such as provided by Coxeter in Regular Complex Polytopes, (Cambridge Univ. Press 1991) probably because the facilities were not available. The tetrahedron, cube and icosahedron are all Platonic solids which the ancient Greeks recognised as basic to the construction of the physical universe and their finite symmetries are the basis of considerable study in particle physics today. Interestingly enough I plotted Klein's equation for the tetrahedron (using a computer program unavailable in 1884)and found a cube which is well-known to be isomorphic to the tetrahedron.

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