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.

We are what we eat, as the saying goes, but we are also how we eat, and when, and where. Our eating habits reveal as much about our society as the food on our plates, and our national identity is written in the eating schedules we follow and the customs we observe at the table and on the go. In Three Squares, food historian Abigail Carroll upends the popular understanding of our most cherished mealtime traditions, revealing that our eating habits have never been stable—far from it, in fact. The eating patterns and ideals we’ve inherited are relatively recent inventions, the products of complex social and economic forces, as well as the efforts of ambitious inventors, scientists and health gurus. Whether we’re pouring ourselves a bowl of cereal, grabbing a quick sandwich, or congregating for a family dinner, our mealtime habits are living artifacts of our collective history—and represent only the latest stage in the evolution of the American meal. Our early meals, Carroll explains, were rustic affairs, often eaten hastily, without utensils, and standing up. Only in the nineteenth century, when the Industrial Revolution upset work schedules and drastically reduced the amount of time Americans could spend on the midday meal, did the shape of our modern “three squares” emerge: quick, simple, and cold breakfasts and lunches and larger, sit-down dinners. Since evening was the only part of the day when families could come together, dinner became a ritual—as American as apple pie. But with the rise of processed foods, snacking has become faster, cheaper, and easier than ever, and many fear for the fate of the cherished family meal as a result. The story of how the simple gruel of our forefathers gave way to snack fixes and fast food, Three Squares also explains how Americans’ eating habits may change in the years to come. Only by understanding the history of the American meal can we can help determine its future.

This board book full of squares and clever cut-outs is a wonderful way to introduce babies and toddlers to shapes. Is it a door? A book? A train or a present? Read aloud and create a clever guessing game about shapes that will delight and stimulate the youngest readers. Squares and rectangles are everywhere, and the shapes and colors found in everyday objects come to life when the pages of the book are turned. Learning shapes is a lot of fun when there are surprises involved—this die-cut board book from master artist and designer Yusuke Yonezu is full of them.

Forty outstanding urban spaces of the Western world, analyzed and drawn at a common scale for easy comparison.

From the dream team of Jon Klassen and Mac Barnett comes the second instalment in the exciting new shape trilogy. Every day, Square brings a block out of his cave and pushes it up a steep hill. This is his work. When Circle floats by, she declares Square a genius, a sculptor! “This is a wonderful statue,” she says. “It looks just like you!” But now Circle wants a sculpture of her own, a circle! Will the genius manage to create one? Even accidentally?

This volume is based on lectures delivered at the 2019 AMS Short Course “Sum of Squares: Theory and Applications”, held January 14–15, 2019, in Baltimore, Maryland. This book provides a concise state-of-the-art overview of the theory and applications of polynomials that are sums of squares. This is an exciting and timely topic, with rich connections to many areas of mathematics, including polynomial and semidefinite optimization, real and convex algebraic geometry, and theoretical computer science. The six chapters introduce and survey recent developments in this area; specific topics include the algebraic and geometric aspects of sums of squares and spectrahedra, lifted representations of convex sets, and the algorithmic and computational implications of viewing sums of squares as a meta algorithm. The book also showcases practical applications of the techniques across a variety of areas, including control theory, statistics, finance and machine learning.