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This chapter expands a little on the idea that gravity is geometry, and then describes how the geometry of space and time is a subject for experiment and theory in physics. In a gravitational field, all bodies with the same initial conditions will follow the same curve in space and time. Einstein’s idea was that this uniqueness of path could be explained in terms of the geometry of the four-dimensional union of space and time called spacetime. Specifically, he proposed that the presence of a mass such as Earth curves the geometry of spacetime nearby, and that, in the absence of any other forces, all bodies move on the straight paths in this curved spacetime. We explore how simple three-dimensional geometries can be thought of as curved surfaces in a hypothetical four-dimensional Euclidean space. The key to a general description of geometry is to use differential and integral calculus to reduce all geometry to a specification of the distance between each pair of nearby points.
If education is to prepare learners for lifelong learning, there needs to be a shift towards deeper learning: a focus on transferable knowledge and problem-solving skills alongside the development of a positive or growth mindset. In this book, a follow up to CLIL, the authors review new developments in the understanding of the interface between language and learning, and propose an original new 'pluriliteracies' approach which refines and develops current thinking in CLIL. It aims to facilitate deeper learning through an explicit focus on disciplinary literacies, guiding learners towards textual fluency, encouraging successful communication across cultures, and providing a key stepping-stone towards becoming responsible global citizens. It both provides strong theoretical grounding, and shows how to put that understanding into practise. Engaging and practical, this book will be invaluable to both academics and education practitioners, and will enable conventional classrooms to be transformed into deeper learning ecologies.
The narrative of Roman history has been largely shaped by the surviving literary sources, augmented in places by material culture. The numerous surviving coins can, however, provide new information on the distant past. This accessible but authoritative guide introduces the student of ancient history to the various ways in which they can help us understand the history of the Roman republic, with fresh insights on early Roman-Italian relations, Roman imperialism, urban politics, constitutional history, the rise of powerful generals and much more. The text is accompanied by over 200 illustrations of coins, with detailed captions, as well as maps and diagrams so that it also functions as a sourcebook of the key coins every student of the period should know. Throughout, it demystifies the more technical aspects of the field of numismatics and ends with a how-to guide for further research for non-specialists.
How do dolphins catch fish in murky water? Why do moths drink from puddles? How do birds' eggs breathe? How do animals work? In this revised and updated edition of the acclaimed text Animal Physiology, the answers are revealed. In clear and stimulating style, Knut Schmidt-Nielsen introduces and develops the fundamental principles of animal physiology according to major environmental features - oxygen, food and energy, temperature, and water. The structure of the book is unchanged from the previous edition, but every chapter has been updated to take into account recent developments, with numerous new references and figures. Animal Physiology is suitable as a text for undergraduate and beginning graduate courses in physiology. As with previous editions, students, teachers as well as researchers will find this book a valuable and enjoyable companion to course work and research.
The climate surrounding foreign investment law is one of controversy and change, and with implications for human rights and environmental protection, foreign investment law has gained widespread public attention and visibility. This fully updated edition of Sornarajah's classic text offers thought-provoking analysis of the law in historical, political and economic contexts, capturing leading trends and charting the possible course of future developments. It takes into account the newer types of treaties that establish a regulatory space for states and moves away from inflexible investment protection, exploring the newly created defences relating to environment, human rights, indigenous rights and other areas ending the fragmentation of the law. It looks at the current debates on legitimacy of the system and current efforts at reform. Suitable for postgraduate and undergraduate students, The International Law on Foreign Investment is essential reading for anyone specialising in the law of foreign investments.
Chapter 5 is a unique book chapter. The purpose is to introduce the reader to the array of chemical, physical, and mineralogical data commonly provided by the Natural Resource Conservation Service (NRCS) as well as most international soil survey programs. This database is enormous, containing a wealth of still untapped potential. The chapter provides the reader with a concise overview of what is on the soil characterization data sheets and how the data are obtained. These data then serve as the basis for any number of research questions and explorations.
In this chapter we first consider finite element modeling of slender bodies undergoing bending deformation. This will be followed by a discussion on frame structures which can be modeled as an assemblage of slender bodies rigidly connected. First, we will introduce the Bernoulli--Euler theory of beam bending as a review and extension of what is typically covered in an undergraduate sophomore-level course on mechanics of materials. We will then introduce the frame element which can be used to model frame structures deforming in the 2D plane and 3D space.