This book, a translation of the German volume n-Ecke, presents an elegant geometric theory which, starting from quite elementary geometrical observations, exhibits an interesting connection between geometry and fundamental ideas of modern algebra in a form that is easily accessible to the student who lacks a sophisticated background in mathematics. It stimulates geometrical thought by applying the tools of linear algebra and the algebra of polynomials to a concrete geometrical situation to reveal some rather surprising insights into the geometry of n-gons. The twelve chapters treat n-gons, classes of n-gons, and mapping of the set of n-gons into itself. Exercises are included throughout, and two appendixes, by Henner Kinder and Eckart Schmidt, provide background material on lattices and cyclotomic polynomials.

(Mathematical Expositions No. 18)

Friedrich Bachmann (1909-1982) was at the Christian Albrechts University in Kiel.

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Eckart Schmidt was at the Christian Albrechts University in Kiel.

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Cyril W.L.Garner is a professor emeritus in the Department of Mathematics at Carleton University.

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