Shadows Of The Circle: Conic Sections, Optimal Figures And Non-Euclidean Geometry - Hardcover

Hansen, Vagn Lundsgaard

Hardcover

ISBN 10: 981023418X ISBN 13: 9789810234188

Publisher: Wspc, 1998

Synopsis

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 Poincaré disc model of the hyperbolic plane is developed.

About this title

Synopsis

This work offers insights on various facets of geometry through development of four geometric themes: ellipse, the shape or shadow cast by a cirlce; all three types of conic sections - the ellipse, the parabola and the hyperbola; certain properties of geometric figures related to the problem of finding the largest areas that can be enclosed by a curve of given length - the isoperimetric problem; and a development of the non-Euclidean geometry in the Poincare disc model of the hyperbolic plane.

Edition details

• Publisher: Wspc
• Publication date: 1998
• Language: English
• ISBN 10: 981023418X
• ISBN 13: 9789810234188
• Binding: Hardcover
• Number of pages: 120