Claiming Land, Claiming Water shares what historians and geographers wish readers knew about maps and borders before, during, and after the founding of the United States. The essays collected in this volume model how people can learn to interpret maps as arguments, rather than as historical facts, and to read maps for evidence of people and places that were elided, renamed, or destroyed. Contributors travel through the sixteenth, seventeenth, eighteenth, and nineteenth centuries in the place known by many names: the Atlantic World; the North American continent; borderlands; and homelands. Onto this place where people exercised power over space by forging relationships, colonizers came and imagined borders onto maps. Featuring reproductions of twenty historical maps, the book takes readers through this era of immense disruption to teach them strategies for reading and interpreting these maps critically. Essays attend carefully to water alongside land and land alongside water in search of new interpretive avenues that reframe what we know about space, control, and sovereignty. By using historical examples of people--farmers, fishers, hunters, religious leaders, colonial projectors, traders, sailors, soldiers, diplomats, and cartographers, it becomes possible to resist the temptation to impose modern geographical constructs backwards onto the histories we read, teach, and write. Claiming Land, Claiming Water investigates why some of these people imagined and made claims to bounded space, and how and why other people confounded and challenged those claims. Contributors: Sarah Chute, Edward G. Gray, Kim M. Gruenwald, Rachel B. Herrmann, Christian J. Koot, Chad McCutchen, Jennifer Monroe McCutchen, John Morton, Paul Musselwhite, Charles Prior, Karen Rann, Jessica Choppin Roney, Samuel Truett, Harvey Amani Whitfield, Alex Zukas.
Polyhedra are used in several fields by mathematicians and other scientists. It is easy to think of examples from architecture. Polyhedra have been used to scientifically explain the world around us. In the early days of study, polyhedra included only convex polyhedra. Since the ancient Greeks, many thinkers have worked on convex polyhedra. There are only five regular convex polyhedra known as Platonic solids, thirteen semi-regular convex polyhedra known as Archimedean solids, and thirteen irregular convex polyhedra which are duals of the Archimedean solids and known as Catalan solids. In this study, we show that the isometry group of the threedimensional analytic space formed by the metrics of the Tetrakis hexahedron and the Disdyakis dodecahedron is the semi-direct product of Oh and T(3), where the octahedral group Oh is the (Euclidean) symmetry group of the octahedron and T(3) is the group of all translations of the three-dimensional space.
The Lane-Emden equations have been used to model some phenomena in astrophysics, such as mathematical physics and stellar structure theory. In addition, the Lane-Emden equation is a central equation in the theory of stellar structures. In this paper, we introduce the Lane-Emden differential equations. A special second order Lane-Emden differential equation is solved by He’s variational iteration, adomian decomposition method, homotopy analysis method, homotopy perturbation method, and finite difference method respectively. The results obtained are compared with each other and it is analyzed which method gives more reliable results and is more useful than the others.
Many generalizations of the traditional metric space have been introduced in the literature, such as 2−, D−, G−, S− and b−metric spaces. When the studies on these generalized metric spaces are examined, it is seen that the main motivation of the researchers is to develop and generalize the famous Banach fixed point theorem. Although introduced with a similar motivation, its ability to measure the distance between n points simultaneously distinguishes the n th order G−metric space from other generalized metric spaces. In this study, we will give new and original fixed point theorems that reveal the importance of G−metric techniques since they cannot be reduced to the framework of quasi and conventional metric spaces.
Minkowski geometry is a non-Euclidean geometry in a finite number of dimensions. In a Minkowski geometry the unit ball is a symmetric, convex closed set instead of the usual sphere in Euclidean space. In [14], it is shown that there are some geometries which unit spheres are cuboctahedron and truncated octahedron-which are Archimedean solids-, they are also Minkowski geometries. In geometry determining the group of isometries of a space with a metric is a fundamental problem. In this article we show that the group of isometries of the 3−dimensional spaces covered by CO − metric and TO − metric are the semi-direct product of Oh and T(3), where octahedral group Oh is the (Euclidean) symmetry group of the octahedron and T(3) is the group of all translations of the 3−dimensional space.
