Whereas conventional maps can be expressed as outward-expanding formulae with well-defined central features and relatively poorly defined edges, Constant Scale Natural Boundary (CSNB) maps have well-defined boundaries that result from natural processes and thus allow spatial and dynamic relationships to be observed in a new way useful to understanding these processes. CSNB mapping presents a new approach to visualization that produces maps markedly different from those produced by conventional cartographic methods. In this approach, any body can be represented by a 3D coordinate system. For a regular body, with its surface relatively smooth on the scale of its size, locations of features can be represented by definite geographic grid (latitude and longitude) and elevation, or deviation from the triaxial ellipsoid defined surface. A continuous surface on this body can be segmented, its distinctive regional terranes enclosed, and their inter-relationships defined, by using selected morphologically identifiable relief features (e.g., continental divides, plate boundaries, river or current systems). In this way, regions of distinction on a large, essentially spherical body can be mapped as two-dimensional ‘facets’ with their boundaries representing regional to global-scale asymmetries (e.g., continental crust, continental and oceanic crust on the Earth, farside original thicker crust and nearside thinner impact punctuated crust on the Moon). In an analogous manner, an irregular object such as an asteroid, with a surface that is rough on the scale of its size, would be logically segmented along edges of its impact-generated faces. Bounded faces are imagined with hinges at occasional points along boundaries, resulting in a foldable ‘shape model.’ Thus, bounded faces grow organically out of the most compelling natural features. Obvious boundaries control the map’s extremities, and peripheral regions are not dismembered or grossly distorted as in conventional map projections. 2D maps and 3D models grow out of an object’s most obvious face or terrane ‘edges,’ instead of arbitrarily by imposing a regular grid system or using regularly shaped facets to represent an irregular surface.

• A New Republic Best Book of the Year • The Globalist Top Books of the Year • Winner of the Maine Literary Award for Non-fiction Particularly relevant in understanding who voted for who during presidential elections, this is an endlessly fascinating look at American regionalism and the eleven “nations” that continue to shape North America According to award-winning journalist and historian Colin Woodard, North America is made up of eleven distinct nations, each with its own unique historical roots. In American Nations he takes readers on a journey through the history of our fractured continent, offering a revolutionary and revelatory take on American identity, and how the conflicts between them have shaped our past and continue to mold our future. From the Deep South to the Far West, to Yankeedom to El Norte, Woodard (author of American Character: A History of the Epic Struggle Between Individual Liberty and the Common Good) reveals how each region continues to uphold its distinguishing ideals and identities today, with results that can be seen in the composition of the U.S. Congress or on the county-by-county election maps of any hotly contested election in our history.

Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.