The Squares

The Book of Squares by Fibonacci is a gem in the mathematical literature and one of the most important mathematical treatises written in the Middle Ages. It is a collection of theorems on indeterminate analysis and equations of second degree which yield, among other results, a solution to a problem proposed by Master John of Palermo to Leonardo at the Court of Frederick II. The book was dedicated and presented to the Emperor at Pisa in 1225. Dating back to the 13th century the book exhibits the early and continued fascination of men with our number system and the relationship among numbers with special properties such as prime numbers, squares, and odd numbers. The faithful translation into modern English and the commentary by the translator make this book accessible to professional mathematicians and amateurs who have always been intrigued by the lure of our number system.

When ungroovy scientists did groovy science: how non-activist scientists and engineers adapted their work to a rapidly changing social and political landscape. In The Squares, Cyrus Mody shows how, between the late 1960s and the early 1980s, some scientists and engineers who did not consider themselves activists, New Leftists, or members of the counterculture accommodated their work to the rapidly changing social and political landscape of the time. These “square scientists,” Mody shows, began to do many of the things that the counterculture urged: turn away from military-industrial funding, become more interdisciplinary, and focus their research on solving problems of civil society. During the period Mody calls “the long 1970s,” ungroovy scientists were doing groovy science. Mody offers a series of case studies of some of these collective efforts by non-activist scientists to use their technical knowledge for the good of society. He considers the region around Santa Barbara and the interplay of public universities, think tanks, established firms, new companies, philanthropies, and social movement organizations. He looks at Stanford University’s transition from Cold War science to commercialized technoscience; NASA’s search for a post-Apollo mission; the unsuccessful foray into solar energy by Nobel laureate Jack Kilby; the “civilianization” of the US semiconductor industry; and systems engineer Arthur D. Hall’s ill-fated promotion of automated agriculture.

Latin Squares and Their Applications, Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader ‘from the beginnings of the subject to the frontiers of research’. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the end of the first edition is discussed and commented upon. In addition, a number of new unsolved problems are proposed. Using an engaging narrative style, this book provides thorough coverage of most parts of the subject, one of the oldest of all discrete mathematical structures and still one of the most relevant. However, in consequence of the huge expansion of the subject in the past 40 years, some topics have had to be omitted in order to keep the book of a reasonable length. Latin squares, or sets of mutually orthogonal latin squares (MOLS), encode the incidence structure of finite geometries; they prescribe the order in which to apply the different treatments in designing an experiment in order to permit effective statistical analysis of the results; they produce optimal density error-correcting codes; they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. As regards more recreational aspects of the subject, latin squares provide the most effective and efficient designs for many kinds of games tournaments and they are the templates for Sudoku puzzles. Also, they provide a number of ways of constructing magic squares, both simple magic squares and also ones with additional properties. Retains the organization and updated foundational material from the original edition Explores current and emerging research topics Includes the original 73 ‘Unsolved Problems’ with the current state of knowledge regarding them, as well as new Unsolved Problems for further study

The science of magic squares witnessed an important development in the Islamic world during the Middle Ages, with a great variety of construction methods being created and ameliorated. The initial step was the translation, in the ninth century, of an anonymous Greek text containing the description of certain highly developed arrangements, no doubt the culmination of ancient research on magic squares.

Of the many types of historic landscapes that have become treasured open spaces in North America's dense urban fabric, the garden (or residential) square largely has been overlooked. Yet the garden square played an important role in the planning of Philadelphia, Savannah, Boston, and New York, several of America's major early cities. Boston's garden squares most closely resemble the squares of London in purpose and appearance. Intended as speculative real estate ventures, the London garden squares were distinguished by row houses and ornamental iron fences enclosing gardens planted with trees and grass. The gardens served as welcome patches of greenery for affluent residents who chose to live in relatively cramped quarters within the city. As such, gardens were the raison d'etre for this early form of urban design. Although garden squares pre-date well-documented municipal parks, the historical significance of these squares is not fully understood. In this remarkable book, Goodman tells the story of Boston's garden squares and offers her readers a fascinating glimpse of early urban planning. Goodman traces Charles Bulfinch's connection with these historic landscapes and compares them to their London prototypes. While Bostonians and others are familiar with Boston's iconic Louisburg Square on Beacon Hill, few people know that Boston's South End neighborhood boasts a group of eight garden squares. After discussing London squares and their effect on urban planning in several eastern seaboard cities, Goodman turns to Boston's three privately developed garden squares, all of which were located close to the original center of the city. She pays special attention to Louisburg Square, the only one that has survived. Focusing on the characteristic landscape features that define the gardens, Goodman also showcases the five of the eight publicly developed garden squares of the South End--Blackstone Square, Franklin Square, Chester Square, Union Park, and Worcester Square. Concluding with a chapter on the evolution and preservation of the garden squares of the South End, Goodman discusses private versus public ownership and access, maintenance, and preservation treatments--issues that provide practical information helpful in the management of historical as well as contemporary landscapes. She urges a combined effort of neighborhood groups and the public sector to maintain these squares. Otherwise, she warns, "the future of these historic garden squares will be in jeopardy."

Delves into the strange, quirky and curious histories of London's famous squares.

The Square Planet combines comedy, drama, science fiction, suspense, music & singing, and even geometry lessons to present a heartwarming parable about the value of diversity and tolerance. Presented as a play by seven groups of San Franscisco Bay Area children (ages 7-8) before this book was conceived.