Shadows of the circle : conic sections, optimal figures and non-euclidean geometry

著者

• Hansen, Vagn Lundsgaard

書誌事項

Shadows of the circle : conic sections, optimal figures and non-euclidean geometry

Vagn Lundsgaard Hansen

World Scientific, c1998

注記

Includes bibliographical references and index

内容説明・目次

内容説明

The aim of this book is to throw light on various facets of geometry through development of four geometrical themes.The first theme is about the ellipse, the shape of the shadow cast by a circle. The next, a natural continuation of the first, is a study of all three types of conic sections, the ellipse, the parabola and the hyperbola.The third theme is about certain properties of geometrical figures related to the problem of finding the largest area that can be enclosed by a curve of given length. This problem is called the isoperimetric problem. In itself, this topic contains motivation for major parts of the curriculum in mathematics at college level and sets the stage for more advanced mathematical subjects such as functions of several variables and the calculus of variations.The emergence of non-Euclidean geometries in the beginning of the nineteenth century represents one of the dramatic episodes in the history of mathematics. In the last theme the non-Euclidean geometry in the Poincare disc model of the hyperbolic plane is developed.

目次

• An ellipse in the shadow
• with conic sections in the light
• optimal plane figures
• the Poincare disc model of non-Euclidean geometry
• exercises.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA36242785
• ISBN:
  • 981023418X
• LCCN: 97036352
• 出版国コード: si
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Singapore
• ページ数/冊数: viii, 111 p.
• 大きさ: 23 cm