By Robin Hartshorne

ISBN-10: 1441931457

ISBN-13: 9781441931450

This publication deals a different chance to appreciate the essence of 1 of the nice thinkers of western civilization. A guided studying of Euclid's components results in a severe dialogue and rigorous smooth remedy of Euclid's geometry and its more moderen descendants, with entire proofs. themes contain the advent of coordinates, the speculation of zone, historical past of the parallel postulate, many of the non-Euclidean geometries, and the commonplace and semi-regular polyhedra.

Show description

Read or Download Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics) PDF

Best geometry books

Werner Ballmann's Lectures on Kähler Manifolds (Esi Lectures in Mathematics PDF

Those notes are in line with lectures the writer gave on the collage of Bonn and the Erwin Schrödinger Institute in Vienna. the purpose is to offer a radical advent to the speculation of Kähler manifolds with distinctive emphasis at the differential geometric facet of Kähler geometry. The exposition starts off with a brief dialogue of complicated manifolds and holomorphic vector bundles and an in depth account of the elemental differential geometric homes of Kähler manifolds.

Download e-book for iPad: Lectures on Discrete Geometry by Jiří Matoušek (auth.), Jiří Matoušek (eds.)

Discrete geometry investigates combinatorial homes of configurations of geometric gadgets. To a operating mathematician or desktop scientist, it deals refined effects and strategies of serious range and it's a starting place for fields corresponding to computational geometry or combinatorial optimization.

Read e-book online Discrete Geometry for Computer Imagery: 10th International PDF

This e-book constitutes the refereed complaints of the tenth overseas convention on electronic Geometry for desktop Imagery, DGCI 2002, held in Bordeaux, France, in April 2002. The 22 revised complete papers and thirteen posters provided including three invited papers have been rigorously reviewed and chosen from sixty seven submissions.

Additional resources for Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)

Sample text

The axiom that halves of equals are equal to conclude the triangles have equal content. 42 1. 47), the theorem of Pythagoras. The statement of the theorem is that if ABC is a right K triangle, then the squares on the two legs together have equal content to the square on the hypotenuse. The proof goes like this. The triangle ABF is one half of the square ABFG. 37). The triangle BFC is congruent to the triangle BAD. 37). This latter triangle is equal to one-half of the rectangle BDLM. Hence the square ABFG has equal content to the rectangle BDLM.

A .... 9 Construct a circle inscribed in a given triangle ABC (par = 13). , \ / c.. 2. 10 Construct a circle circumscribed about a given triangle ABC (par = 7). 11 Given a line 1, a line segment d, and a point 0, construct a circle with center o that cuts off a segment congruent to d on the line 1 (par = 9). ~,,- - , t.. - - - \ I on 1, construct a circle that passes through A and is tangent to the line 1 at B (par = 8). B I \ , A\ ......... e ,.. 13 Construct three circles, each one meeting the other two at right angles.

Ruler and Compass Constructions 23 exact. In other words, it must be possible to prove using the reasoning of abstract geometry that this construction in its ideal form gives the exact result we are seeking. This distinction has caused considerable confusion among amateur mathematicians through the ages, who were trying to make constructions, now known to be impossible, of trisecting the angle or squaring the circle . For many of their constructions are remarkably accurate, while failing to be mathematically exact.

Download PDF sample

Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics) by Robin Hartshorne

by Joseph

Rated 4.73 of 5 – based on 13 votes