The Shapes Of Things
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The Shapes of Things
Many things around us have properties that depend on their shape--for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a "shape variable." This approach, which is useful for understanding mathematical models containing geometric partial differential equations (PDEs), allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts. Readers will learn how to compute sensitivities with respect to geometry by developing basic calculus tools on surfaces and combining them with the calculus of variations. Several applications that utilize shape derivatives and many illustrations that help build intuition are included.
The Shape of Things
Discusses and illustrates many shapes including circles and ovals, squares and rectangles, triangles and pyramids, stars and crescents. Includes information on spirals, pattern, and symmetry.
The Shape of Things
By the Author of the Martian Chronicles and Fahrenheit 451. He did not want to be the father of a small blue pyramid. Peter Horn hadn’t planned it that way at all. Neither he nor his wife imagined that such a thing could happen to them. They had talked quietly for days about the birth of their coming child, they had eaten normal foods, slept a great deal, taken in a few shows, and, when it was time for her to fly in the helicopter to the hospital, her husband, Peter Horn, laughed and kissed her.