Volume 12 of the Math-Art series. This 3-part book is a visual exploration of knot geometry and ethnomathematics to celebrate the similarities between abstract geometry and unique cultures worldwide. Starting at latitude 0º, longitude 0º, the author set sail (virtually) westward at an average of 400 (nautical) knots a week to fully cover its circumference and explore 1 new knot each week for an entire year. Part I is the art portfolio extracted from the geometry models, part II is a detailed record of the original geometry used to create the artwork, and part III is the weekly wind map log showing the project’s positioning, actual winds, and currents in real-time. Each book includes 52 illustrations, notes, and references.

Volume 12 of the Math-Art series. This 3-part book is a visual exploration of knot geometry and ethnomathematics to celebrate the similarities between abstract geometry and unique cultures worldwide. Starting at latitude 0º, longitude 0º, the author set sail (virtually) westward at an average of 400 (nautical) knots a week to fully cover its circumference and explore 1 new knot each week for an entire year. Part I is the art portfolio extracted from the geometry models, part II is a detailed record of the original geometry used to create the artwork, and part III is the weekly wind map log showing the project’s positioning, actual winds, and currents in real-time. Each book includes 52 illustrations, notes, and references.

Volume 12 of the Math-Art series. This 3-part book is a visual exploration of knot geometry and ethnomathematics to celebrate the similarities between abstract geometry and unique cultures worldwide. Starting at latitude 0º, longitude 0º, the author set sail (virtually) westward at an average of 400 (nautical) knots a week to fully cover its circumference and explore 1 new knot each week for an entire year. Part I is the art portfolio extracted from the geometry models, part II is a detailed record of the original geometry used to create the artwork, and part III is the weekly wind map log showing the project’s positioning, actual winds, and currents in real-time. Each book includes 52 illustrations, notes, and references.

The 52 Illustration Prime Number series is a new chapter in the ongoing Math-Art collection exploring the world of mathematics and art. Inspired by the research of mathematicians from yesterday and today, this project aims to explore the visual aspect of numbers and highlight the unexpected connections between the challenging world of calculus, geometry, and art. Some will find references to ethnomathematics or a reflection on the universal cross-cultural appeal of mathematics; others will find a relation with the world we’re mapping for tomorrow, and hopefully, all will enjoy this unexpected interpretation of numbers from an artistic standpoint.

A 52 illustration two-part book on the exploration of minimal surfaces. Part 1 explores the surface from an artistic perspective, and part 2 visually reproduces the equations that stand in their own right as a beautiful expression of pure geometry. Each book includes notes from an informal work-in-progress diary and references directing the reader to the images’ original mathematical source. Both sides complement each other in helping us appreciate better these unrivaled expressions of our environment found in nature, from butterflies to black holes, and studied in statistics, material sciences, and architecture.

Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

A 52-illustration, notes, and references book exploring the geometry of H. Coxeter surfaces. Coxeter was instrumental in many discoveries in the field of geometry and computer sciences. He opened the door to the 4th dimension to all studying higher spaces. Exploring these groups has some practical applications in mineralogy, architecture, linear programming, and other areas; mostly, people enjoy contemplating the figures because of their symmetrical shapes and aesthetic appeal. For artists, it is a limitless trove of inspiration. This illustrated book results from some of the most striking Coxeter examples of geometry in higher dimensions.

A groundbreaking look at the phenomenon of the labyrinth, connecting this ancient symbol to modern scientific principles. • Illustrated with labyrinths from around the world and throughout history. • Demonstrates how the labyrinth differs from a maze and how it is a tool for interpreting ancient myths and religious beliefs. • Draws parallels between the labyrinth and quantum physics, showing how through the secrets of the labyrinth we can unlock the mystery of life itself. The powerful symbol of the labyrinth exists in countless cultures spanning the globe from Africa and ancient Greece to India, China, and pre-Colombian North and South America. For centuries they have been used for religious rituals, meditation, and spiritual and physical healing. In the labyrinth humanity finds a model of the quintessential sacred space that depicts the most profound levels of consciousness. Its center is regarded in many cultures as a door between two worlds, thus providing individuals with the ideal place for self questioning and meditation. In a comprehensive exploration of this time-honored symbol, Patrick Conty shows how the geometrical construction of the ancient labyrinth corresponds exactly with today's modern geometry, illustrating that recent developments in math and physics parallel the science of ancient civilizations. By looking at the way the two systems complement each other, Conty draws new conclusions about the ancient world and how that world can benefit us right now. Conty explores not only physical labyrinths but also reveals how the same transcendent principles are at work in Celtic knot work; the designs of ancient Chinese cauldrons; the tattoos and tracings of primitive art; the textiles of Africa, Peru, and Central America; and the geometric patterns in Islamic art.

Beckett, Lacan and the Mathematical Writing of the Real proposes writing as a mathematical and logical operation to build a bridge between Lacanian psychoanalysis and Samuel Beckett's prose works. Arka Chattopadhyay studies aspects such as the fundamental operational logic of a text, use of mathematical forms like geometry and arithmetic, the human obsession with counting, the moving body as an act of writing and love, and sexuality as a challenge to the limits of what can be written through logic and mathematics. Chattopadhyay reads Beckett's prose works, including How It Is, Company, Worstward Ho, Malone Dies and Enough to highlight this terminal writing, which halts endless meanings with the material body of the word and gives Beckett a medium to inscribe what cannot be written otherwise.

For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).