What Are The Basic Tools Of Euclidean Geometry
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Computing In Euclidean Geometry
This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. The topics covered are: a history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra; triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and steiner trees. Each chapter is written by a leading expert in the field and together they provide a clear and authoritative picture of what computational Euclidean geometry is and the direction in which research is going.
Geometry: Euclid and Beyond
Author: Robin Hartshorne
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-11-11
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. For a one-semester course such as I teach, Chapters 1 and 2 form the core material, which takes six to eight weeks.
On Folding
Author: Michael Friedman
language: en
Publisher: transcript Verlag
Release Date: 2016-05-15
It is only recently, with the increasing interest in origami and folding in natural sciences and the humanities, that the fold as a new conception in a whole range of disciplines has begun to be conceived in a broader way. Folding as a material and structural process offers a new methodology to think about the close relationship of matter, form and code. It henceforth crosses out old dichotomies, such as the organic and the inorganic or nature and technology, and blurs the boundaries between experimental, conceptual and historical approaches. This anthology aims to unfold this new interdisciplinary field and its disciplinary impact, ranging from materials science, biology, architecture, and mathematics to literature and philosophy.