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
east 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.
Here, three types of conic section are discussed briefly.
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.
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