"In 1611, Kepler wrote an essay wondering why snowflakes always had perfect, sixfold symmetry. It's a simple enough question, but one that no one had ever asked before and one that couldn't actually be answered for another three centuries. Still, in trying to work out an answer, Kepler raised some fascinating questions about physics, math, and biology, and now you can watch in wonder as a great scientific genius unleashes the full force of his intellect on a seemingly trivial question, complete with new illustrations and essays to put it all in perspective."—io9, from their list "10 Amazing Science Books That Reveal The Wonders Of The Universe" When snow began to fall while he was walking across the Charles Bridge in Prague late in 1610, the eminent astronomer Johannes Kepler asked himself the following question: Why do snowflakes, when they first fall, and before they are entangled into larger clumps, always come down with six corners and with six radii tufted like feathers? In his effort to answer this charming and never-before-asked question about snowflakes, Kepler delves into the nature of beehives, peapods, pomegranates, five-petaled flowers, the spiral shape of the snail's shell, and the formative power of nature itself. While he did not answer his original question—it remained a mystery for another three hundred years—he did find an occasion for deep and playful thought. "A most suitable book for any and all during the winter and holiday seasons is a reissue of a holiday present by the great mathematician and astronomer Johannes Kepler…Even the endnotes in this wonderful little book are interesting and educationally fun to read."—Jay Pasachoff, The Key Reporter —New English translation by Jacques Bromberg —Latin text on facing pages —An essay, "The Delights of a Roving Mind" by Owen Gingerich —An essay, "On The Six-Cornered Snowflake" by Guillermo Bleichmar —Snowflake illustrations by Capi Corrales Rodriganez —John Frederick Nims' poem "The Six-Cornered Snowflake" —Notes by Jacques Bromberg and Guillermo Bleichmar

Kepler's essay, On the Six-Cornered Snowflake, provides the first published evidence of the ideas of regular arrangements and close-packing which have proved fundamental to crystallography. In it, Kepler ponders on the problem of why snowflakes are hexagonal, two centuries before the first successful steps were taken towards its solution. The purpose of this volume is to display the historical, literary, scientific, and philosophical treasures of Kepler's essay. The book includes the modernized text of the 1611 Latin edition, with an English translation by Colin Hardie on the opposite pages. The text is accompanied by an introduction giving details of the history of the work, and two essays; Professor B. J. Mason's discussion of the scientific meaning and validity of Kepler's arguments and their relation to the history of crystallography and of space filling, and L. L. Whyte's examination of Kepler's facultas formatrix in relation to the history of philosophical and scientific ideas on the genesis of forms.

As a preeminent modernist poet and translator of the classics, John Frederick Nims's work is an elegant fusion of contemporary sensibility with formalist experimentation. But form, for this writer of meditative verse, is only a helpmeet to the quintessential content of the poem, the meaning that gives it value in our time and, one hopes, beyond. Concerning the formal elements of poetry, Nims comments: "One might say they are like the scaffolding at a construction site, meant to be thrown away and not regarded once the building is completed." In his newest collection, The Six-Cornered Snowflake, his poems range through an astonishing variety of complex structures: the shaped-poem of the title work, the sestina, the vocal "Pindar's lattice" of the "First Olympian Ode," the nervous galliambics of "Catullus 63"--just to name a few. As William Pritchard, writing for The New York Times Book Review, so aptly observed, "Mr. Nims has consistently had the nerve to be interested in what language could be made to do, rather than what the psyche would be made to reveal."

A 1988 classic, covering Two-dimensional Surfaces; Domains on the Plane and on Surfaces; Brunn-Minkowski Inequality and Classical Isoperimetric Inequality; Isoperimetric Inequalities for Various Definitions of Area; and Inequalities Involving Mean Curvature.

The cosmology of Johannes Kepler remains a mystery. On the one hand, Kepler’s speculations on spiritual faculties are seen as the remnants of Renaissance philosophy. On the other, his comparison of the cosmos to a clock summons the mechanical metaphor that shaped modern science. This book explores the inseparable connections between Kepler’s vitalistic views and his more enduring accomplishments in astronomy. The key argument is that Kepler’s ‘celestial biology’ served as a bridge between his revolutionary astronomy and other ‘less scientific’ interests, particularly astrology. Kepler's Cosmological Synthesis sheds new light on one of the foundational figures of the Scientific Revolution. By uncovering a new form of coherence in Kepler’s world picture, it traces the unlikely intersections of mechanism and vitalism that transformed the fabric of the heavens.

Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.

“A thrilling, fast-paced excursion through the history of physical discovery . . . from silly putty to string theory” (Dr. Paul Halpern, author of Collider). Following his previous volumes, The Science Book and The Math Book, acclaimed science writer Clifford Pickover returns with a richly illustrated chronology of physics, containing 250 short, entertaining, and thought-provoking entries. In addition to exploring such engaging topics as dark energy, parallel universes, the Doppler effect, the God particle, and Maxwells demon, The Physics Book extends back billions of years to the hypothetical Big Bang and forward trillions of years to a time of “quantum resurrection.” Like the previous titles in this series, The Physics Book offers a lively and accessible account of major concepts without getting bogged down in complex details.

'A wonderful book: Nancy Campbell is a fine storyteller with a rare physical intelligence. The extraordinary brilliance of her eye confers the reader a total immersion in the rimy realms she explores. Glaciers, Arctic floe, verglas, frost and snow -- I can think of no better or warmer guide to the icy ends of the Earth' Dan Richards, author of Climbing Days A vivid and perceptive book combining memoir, scientific and cultural history with a bewitching account of landscape and place, which will appeal to readers of Robert Macfarlane, Roger Deakin and Olivia Laing. Long captivated by the solid yet impermanent nature of ice, by its stark, rugged beauty, acclaimed poet and writer Nancy Campbell sets out from the world's northernmost museum - at Upernavik in Greenland - to explore it in all its facets. From the Bodleian Library archives to the traces left by the great polar expeditions, from remote Arctic settlements to the ice houses of Calcutta, she examines the impact of ice on our lives at a time when it is itself under threat from climate change. The Library of Ice is a fascinating and beautifully rendered evocation of the interplay of people and their environment on a fragile planet, and of a writer's quest to define the value of her work in a disappearing landscape. 'The writer and poet offers reflections on ice and snow that draw on art, science and history... a dreamlike book.' - The Guardian 'It is a sparkling and wonderful meditation on a substance we must cherish' - The Independent 'It is a pleasant brew infused with elements not only of travel and history, but also of memoir and personal reflection'- Literary Review 'Ms Campbell, a penniless but intrepid traveller, braves miserable bus journeys, freezing rain, dark and intense cold, but still manages to write rapturously of the beauties of the Arctic'- The Economist