Shapes and Geometries

Shapes and Geometries
Author: M. C. Delfour
Publisher: SIAM
Total Pages: 637
Release: 2011-01-01
Genre: Mathematics
ISBN: 0898719364

Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.

Shapes and Geometries

Shapes and Geometries
Author: Michel C. Delfour
Publisher: SIAM
Total Pages: 512
Release: 2001-01-01
Genre: Mathematics
ISBN: 9780898714890

The tools to use for problems where the modeling, optimization, or control variable is the structure of a geometric object.

Shapes and Geometries

Shapes and Geometries
Author: M. C. Delfour
Publisher: SIAM
Total Pages: 638
Release: 2011-01-01
Genre: Mathematics
ISBN: 0898719828

This considerably enriched new edition provides a self-contained presentation of the mathematical foundations, constructions, and tools necessary for studying problems where the modeling, optimization, or control variable is the shape or the structure of a geometric object.

The Shapes of Things

The Shapes of Things
Author: Shawn W. Walker
Publisher: SIAM
Total Pages: 156
Release: 2015-06-25
Genre: Mathematics
ISBN: 1611973961

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.

Shape

Shape
Author: Jordan Ellenberg
Publisher: Penguin
Total Pages: 481
Release: 2021-05-25
Genre: Mathematics
ISBN: 1984879065

An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

The Changing Shape of Geometry

The Changing Shape of Geometry
Author: Mathematical Association of America
Publisher: Cambridge University Press
Total Pages: 572
Release: 2003-01-09
Genre: Mathematics
ISBN: 9780521531627

Collection of popular articles on geometry from distinguished mathematicians and educationalists.

Numerical Geometry of Non-Rigid Shapes

Numerical Geometry of Non-Rigid Shapes
Author: Alexander M. Bronstein
Publisher: Springer Science & Business Media
Total Pages: 346
Release: 2008-09-18
Genre: Computers
ISBN: 0387733019

Deformable objects are ubiquitous in the world surrounding us, on all levels from micro to macro. The need to study such shapes and model their behavior arises in a wide spectrum of applications, ranging from medicine to security. In recent years, non-rigid shapes have attracted growing interest, which has led to rapid development of the field, where state-of-the-art results from very different sciences - theoretical and numerical geometry, optimization, linear algebra, graph theory, machine learning and computer graphics, to mention several - are applied to find solutions. This book gives an overview of the current state of science in analysis and synthesis of non-rigid shapes. Everyday examples are used to explain concepts and to illustrate different techniques. The presentation unfolds systematically and numerous figures enrich the engaging exposition. Practice problems follow at the end of each chapter, with detailed solutions to selected problems in the appendix. A gallery of colored images enhances the text. This book will be of interest to graduate students, researchers and professionals in different fields of mathematics, computer science and engineering. It may be used for courses in computer vision, numerical geometry and geometric modeling and computer graphics or for self-study.

Geometry - Task Sheets Gr. PK-2

Geometry - Task Sheets Gr. PK-2
Author: Mary Rosenberg
Publisher: Classroom Complete Press
Total Pages: 34
Release: 2009-09-01
Genre: Education
ISBN: 155319800X

Help young students get familiar with basic shapes found in Geometry. Our resource provides task and word problems surrounding real-life scenarios. See how many circles, squares and rectangles you can find in the picture. Explain how you would sort the shapes you find. Use different shapes to make a robot or house. Find and name the different shapes. Go on the Internet to find some solid shapes that are made from basic shapes put together. Count the number of sides and corners on each shape. Describe where each shape is found in a picture. Follow instructions to draw shapes in specific locations. Transform a shape by turning it, sliding it, or flipping it. Draw the missing half of a symmetrical shape. The task sheets provide a leveled approach to learning, starting with prekindergarten and increasing in difficulty to grade 2. Aligned to your State Standards and meeting the concepts addressed by the NCTM standards, reproducible task sheets, drill sheets, review and answer key are included.

Number, Shape, & Symmetry

Number, Shape, & Symmetry
Author: Diane L. Herrmann
Publisher: CRC Press
Total Pages: 444
Release: 2012-10-18
Genre: Mathematics
ISBN: 1466554657

Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors' successful work with undergraduate students at the University of Chicago, seventh