SHADOWS OF THE CIRCLE (2ND ED‪)‬

The ancient Greeks were the first to seriously ask for scientific explanations of the panorama of the heavens based on mathematical ideas. Ever since, mathematics has played a major role for human perception and description of the outside physical world, and in a larger perspective for comprehending the universe. This second edition pays tribute to this line of thought and takes the reader on a journey in the mathematical universe from conic sections to mathematical modelling of planetary systems.

In the second edition, the four chapters in the first edition on conic sections (two chapters), isoperimetric problems for plane figures, and non-Euclidean geometry, are treated in four revised chapters with many new exercises added. In three new chapters, the reader is taken through mathematics in curves, mathematics in a Nautilus shell, and mathematics in the panorama of the heavens. In all chapters of the book, the circle plays a prominent role.

This book is addressed to undergraduate and graduate students as well as researchers interested in the geometry of conic sections, including the historical background and mathematical methods used. It features selected important results, and proofs that not only proves but also 'explains' the results.

Contents:
Preface to the Second EditionPreface to the First EditionPreliminary NotionsAn Ellipse in the ShadowWith Conic Sections in the LightOptimal Plane FiguresThe Local Shape of Smooth CurvesMathematics in a Nautilus ShellNon-Euclidean Geometry — The Poincaré Disc ModelThe Panorama of the Heavens — A Source of MathematicsIndex
Readership: Pure mathematicians; applied mathematicians; science educators; professionals from engineering and science, undergraduate and graduate students in mathematics and science; high school students and general readers with mathematical insight.

Reviews of the First Edition:This lively written book shows that even “old fashioned” geometry such as conic sections can be presented in a very attractive form … The text under review maintains a nice balance between informal presentation of mathematical problems, their connections and history on one hand and concrete mathematics on the other. - Mathematical Reviews

The book can be recommended to persons — also non-scientists — who are interested in geometrical aspects and the historical background. - Mathematics Abstracts

Key Features: Offers a complete mathematical treatment of fundamental geometrical shapes like conic sections, spiral curves, and cycloids along with applications of these shapes in the sciences The presentations of the subjects are original at several places, and the subjects are presented in context with their applications and historical settings