Neil deGrasse Tyson

J. Richard Gott

Michael Strauss

Robert J. Vanderbei

"If you go out and simply look up, everything - from the Moon to the planets to the stars to the band of the Milky Way - appears to be pasted on the two-dimensional surface of the dome of the sky. Yet, the story of astronomy as a science is how, over time, astronomers have discovered the cosmos in depth. It is the story of the measurement of position and distance, and how our 2D view of the sky above us evolved into a more sophisticated comprehension of the real 3D depths of space. The distances to the stars were first measured using the parallax effect - that is, by comparing the view from opposite sides of the Earth's orbit. This is the same effect that your brain uses (comparing the views from your left and right eyes) to effortlessly give you depth perception. In this book, the authors present the most spectacular stereo images available in astronomy. (Stereo images are pairs of images of the same object, taken 6 months apart - which, as the Earth turns, means viewed from opposite sides of the Earth's orbit.) Each pair of stereo images, when viewed with a special stereo viewer (to be contained in the book itself), portrays the object in 3D. Each striking 3D picture is accompanied by a caption on the facing page, which tells the story and significance of the image in a mini-essay and points out its interesting features. Rather than a random assortment of astronomical wonders, the pictures are arranged in order of their distance from Earth. The book starts out with the Moon and moves outward through planets, stars, and galaxies, finally reaching the cosmic microwave background radiation (CMB), the most distant thing we can see. The distances of objects are given in light travel times - from 1.3 light-seconds for the Moon to 13.8 billion light-years for the CMB. These distances, along with highlights of how each object was discovered and measured by astronomers, provide a framework and narrative thread for the book, which is carried forward from one caption to the next. At each stage of this outward journey, the reader will learn new and surprising facts about fascinating objects in the depths of space. The book also features an introductory Preface that outlines the story of the discovery of the universe in depth, describes the parallax effect, and provides the background and context for the forthcoming visual tour of the observable universe in 3D"--

A Visual Tour

Welcome to the Universe In 3D

This book focuses largely on constrained optimization. It begins with a substantial treatment of linear programming and proceeds to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Along the way, dynamic programming and the linear complementarity problem are touched on as well. This book aims to be the first introduction to the topic. Specific examples and concrete algorithms precede more abstract topics. Nevertheless, topics covered are developed in some depth, a large number of numerical examples worked out in detail, and many recent results are included, most notably interior-point methods. The exercises at the end of each chapter both illustrate the theory, and, in some cases, extend it. Optimization is not merely an intellectual exercise: its purpose is to solve practical problems on a computer. Accordingly, the book comes with software that implements the major algorithms studied. At this point, software for the following four algorithms is available: The two-phase simplex method The primal-dual simplex method The path-following interior-point method The homogeneous self-dual methods.£/LIST£.

Linear Programming: Foundations and Extensions

Using space photographs and scaled maps, demonstrates the actual size of objects in the cosmos, from Buzz Aldrin's historic footprint on the Moon to the entire visible universe, with a gatefold of the Gott-Juric Map of the Universe.

Robert J. Vanderbei

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