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Non-Euclidean Geometries
"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.
A Panorama of Hungarian Mathematics in the Twentieth Century, I
A glorious period of Hungarian mathematics started in 1900 when Lipót Fejér discovered the summability of Fourier series.This was followed by the discoveries of his disciples in Fourier analysis and in the theory of analytic functions. At the same time Frederic (Frigyes) Riesz created functional analysis and Alfred Haar gave the first example of wavelets. Later the topics investigated by Hungarian mathematicians broadened considerably, and included topology, operator theory, differential equations, probability, etc. The present volume, the first of two, presents some of the most remarkable results achieved in the twentieth century by Hungarians in analysis, geometry and stochastics. The book is accessible to anyone with a minimum knowledge of mathematics. It is supplemented with an essay on the history of Hungary in the twentieth century and biographies of those mathematicians who are no longer active. A list of all persons referred to in the chapters concludes the volume.
Discrete Geometry and Symmetry
This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference “Geometry and Symmetry” in Veszprém, Hungary from 29 June to 3 July 2015. The conference was dedicated to Károly Bezdek and Egon Schulte on the occasion of their 60th birthdays, acknowledging their highly regarded contributions in these fields. While the classical problems of discrete geometry have a strong connection to geometric analysis, coding theory, symmetry groups, and number theory, their connection to combinatorics and optimization has become of particular importance. The last decades have see...
The Fifth Postulate
The great discovery that no one wanted to make It's the dawn of the Industrial Revolution, and Euclidean geometry has been profoundly influential for centuries. One mystery remains, however: Euclid's fifth postulate has eluded for two thousand years all attempts to prove it. What happens when three nineteenth-century mathematicians realize that there is no way to prove the fifth postulate and that it ought to be discarded—along with everything they'd come to know about geometry? Jason Socrates Bardi shares the dramatic story of the moment when the tangible and easily understood world we live in gave way to the strange, mind-blowing world of relativity, curved space-time, and more. "Jason Socrates Bardi tells the story of the discovery of non-Euclidian geometry—one of the greatest intellectual advances of all time—with tremendous clarity and verve. I loved this book." —John Horgan, author, The End of Science and Rational Mysticism "An accessible and engrossing blend of micro-biography, history and mathematics, woven together to reveal a blockbuster discovery." —David Wolman, author of Righting the Mother Tongue and A Left-Hand Turn around the World
Conformal Geometry of Discrete Groups and Manifolds
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, Univ...
The Doctrine of Triangles
An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the ma...
Advances in Computer Graphics Hardware III
This book is a collection of the finalized versions of the papers presented at the third Eurographics Workshop on Graphics Hardware. The diversity of the contributions reflects the widening range of options for graphics hardware that can be exploited due to the constant evolution of VLSI and software technologies. The first part of the book deals with the algorithmic aspects of graphics systems in a hardware-oriented context. Topics are: VLSI design strategies, data distribution for ray-tracing, the advantages of point-driven image generation with respect to VLSI implementation, use of memory and ease of parallelization, ray-tracing, and image reconstruction. The second part is on specific hardware, on content addressable memories and voxel-based systems. The third part addresses parallel systems: massively parallel object-based architectures, two systems in which image generated by individual rendering systems are composited, a transputer-based parallel display processor.
Symmetry through the Eyes of a Chemist
It is gratifying to launch the third edition of our book. Its coming to life testi?es about the task it has ful?lled in the service of the com- nity of chemical research and learning. As we noted in the Prefaces to the ?rst and second editions, our book surveys chemistry from the point of view of symmetry. We present many examples from ch- istry as well as from other ?elds to emphasize the unifying nature of the symmetry concept. Our aim has been to provide aesthetic pl- sure in addition to learning experience. In our ?rst Preface we paid tribute to two books in particular from which we learned a great deal; they have in?uenced signi?cantly our approach to the subject matter of our book. The...
