Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.

Suitable for advanced undergraduate and graduate students of engineering, physics, and mathematics and scientific researchers of all types, this is the first authoritative text on invisibility and the science behind it. More than 100 full-color illustrations, plus exercises with solutions. 2010 edition.

A historical introduction to non-Euclidean geometry.

This book is devoted to a monumental and superbly illuminated very large early fourteenth-century Mamluk Qur'an in muhaqqaq script. It constitutes the final part (Juz' 30) of a superb two-volume Qur'an of which the first volume is preserved in the National Museum in Damascus while the second volume, from which the present section originates, is widely dispersed. Remarkably, here the final part of the Qur'an is reunited with its magnificent and richly decorated double finispieces, thus reassembling what must have been among the most striking and lavishly illuminated sections of the entire manuscript. The high degree of inventiveness along with the overall quality of the manuscript point to the work of a master artist. Especially the geometric proficiency suggests the work of Muhammad ibn Mubadir, one of the leading illuminators in Mamluk Cairo at the turn of the thirteenth century. Although little is known of the life of this artist, his illumination in the Baybars al-Jashnagir Qur'an, now in the British Library, and a Qur'an copied in 1306-10 for an unknown patron, now in the Chester Beatty Library, constitute some of the most celebrated achievements of Mamluk Qur'an illumination.

M.U.S. (Mathematical Uniform Space) is a new number of π (pi), representing the reality of the Universe in which we live. With this number, we created a new geometry, Hyperelliptical Geometry, which will provide the unification of physics, thus uniting the Theory of Relativity and Quantum Theory. A new geometry for a new Mathematics and a new Physics. (ISBN 978-65-00-98107-0).