Présentation par l'éditeur
This book offers a unique opportunity to understand the
essence of one of the great thinkers of western
civilization. A guided reading of Euclid's Elements leads
to a critical discussion and rigorous modern treatment of
Euclid's geometry and its more recent descendants. Also
included are complete proofs, introduction of coordinates,
the theory of area, geometrical constructions and finite
field extensions, history of the parallel postulate, the
various non-Euclidean geometries, and the regular and
semi-regular polyhedra. The text is intended for
junior-senior level mathematics majors. This book offers a
unique opportunitiy to understand the essence of one of the
great thinkers of western civilization. A guided reading of
Eulid's Elements leads to a critical discussion and
rigorous modern treatment of Euclid's geometry and its more
recent descendants, with complete proofs, introduction of
coordinates, the theory of area, geometrical condtructions
and finite field extensions, history of the parallel
postulate, the various non-Eclidean geometries, and the
regular and semi-regular polyhedra. The text is intended
for junior-senior level college mathematics majors.
Contents
Introduction
- Euclid's Geometry.
- Hilbert's Axioms.
- Geometry over Fields.
- Segment Arithmetic.
- Area.
- Construction Problems and Field Extensions.
- Non-Euclidean Geometry.
- Polyhedra.
Appendix
