Solid Shape gives engineers and applied scientists access to the extensive mathematical literature on three dimensional shapes. Drawing on the author's deep and personal understanding of three-dimensional space, it adopts an intuitive visual approach designed to develop heuristic tools of real use in applied contexts.Increasing activity in such areas as computer aided design and robotics calls for sophisticated methods to characterize solid objects. A wealth of mathematical research exists that can greatly facilitate this work yet engineers have continued to "reinvent the wheel" as they grapple with problems in three dimensional geometry. Solid Shape bridges the gap that now exists between technical and modern geometry and shape theory or computer vision, offering engineers a new way to develop the intuitive feel for behavior of a system under varying situations without learning the mathematicians' formal proofs. Reliance on descriptive geometry rather than analysis and on representations most easily implemented on microcomputers reinforces this emphasis on transforming the theoretical to the practical.Chapters cover shape and space, Euclidean space, curved submanifolds, curves, local patches, global patches, applications in ecological optics, morphogenesis, shape in flux, and flux models. A final chapter on literature research and an appendix on how to draw and use diagrams invite readers to follow their own pursuits in threedimensional shape.Jan J. Koenderinck is Professor in the Department of Physics and Astronomy at Utrecht University. Solid Shape is included in the Artificial Intelligence series, edited by Patrick Winston, Michael Brady, and Daniel Bobrow

While piloting his spaceship through the skies, Captain Invincible encounters three-dimensional shapes, including cubes, cylinders, and pyramids.

SOLID SHAPES TEACHING GUIDE

You see solid shapes everywhere! Learn how to identify, name, and describe solid shapes.

Diamonds, cubes, rings, and cylinders—shapes are all around us. How many shapes can you find pictured in this book?

Some solid shapes stack. Some solid shapes roll. Which solid shapes can you use to build?

Our first encounters with math usually come through shapes. Geometry skills are learned from an early age, and readers build upon those first geometry lessons with topics like describing objects using the names of shapes, identifying both two-dimensional and three-dimensional shapes, and composing shapes. Readers are able to explore these essential concepts independently through accessible text and colorful images of both new and familiar shapes. Common two-dimensional and three-dimensional shapes are introduced in this volume, which adheres to standard K.G.A.3 of the Common Core State Standards for Mathematics. This book should be paired with "Is It Flat or Is It Solid?" (9781477720004) from the InfoMax Math Readers Program to provide the alternative point of view on the same topic.