A Vector Space Approach to Geometry (Dover Books on Mathematics) [Paperback]

Melvin Hausner (Author), Mathematics (Author)

Book Description

Publication Date: July 21, 2010 | Series: Dover Books on Mathematics

This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; consideration of the particle problem; more. 1965 edition.

Product Details

• Paperback: 416 pages
• Publisher: Dover Publications (July 21, 2010)
• Language: English
• ISBN-10: 0486404528
• ISBN-13: 978-0486404523
• Product Dimensions: 8.3 x 5.4 x 0.8 inches
• Shipping Weight: 15.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #430,575 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

35 of 35 people found the following review helpful:

5.0 out of 5 stars A useful High School Geometry book for Computer Graphics, December 22, 2000

By 

Shankar N. Swamy (Folsom, CA) - See all my reviews
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This review is from: A Vector Space Approach to Geometry (Dover Books on Mathematics) (Paperback)

This is essentially a high school geometry book; but with a difference - its fully linear algebra based approach. If you are a beginner in computer graphics, and want to review elements of geometry and linear algebra, you will benefit from studying through this book.

The almost four hundred pages book is remarkably readable and is very consistent at that. There are both worked out examples and exercise problems, for each section - which are very useful for self-study or revision.

If you have never had an introduction to linear algebra before, you may have to supplement this with a linear algebra book. But if you have not had a good course in elementary geometry, and your motivation is getting started with elementary Computer Graphics/CAD and the likes, this is a good book for that.

Interspersed with the subject matter discussed at a elementary level, in a useful, stimulating style are small, interesting discussions on such useful and relatively advanced topics as function spaces, fixed point theorem in affine transformation, simplices, symmetries etc. I rarely have seen any of these topics mentioned in a book aimed at this level.

Highly recommended for freshman undergraduates and those without any mathematics experience who want to start in Graphics, CAD, CAGD and the likes. Recommended also for experienced practitioners in Graphics: it is good to review the fundamentals once in a while, and a well written book that is a quick read helps at that!

29 of 30 people found the following review helpful:

5.0 out of 5 stars Perfect for first and second year, or physicists, December 1, 2000

By 

Ken Braithwaite (inkster, MI USA) - See all my reviews
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This review is from: A Vector Space Approach to Geometry (Dover Books on Mathematics) (Paperback)

The basics of the very deep connection between geometry and vector spaces. If you do undergrad math you will see everything in this book during first and second year. But what this book does is fit those bits together. He does this very nicely at an introductory level. If you are not in math, but need to learn some geometryfor a physics course, this will be a useful book.

It is a formal math book, with axioms, but it is strong on motivation and has some quite amusing examples.

Keywords: tangent spaces, determinants, barycentric, linear transformations.

29 of 30 people found the following review helpful:

5.0 out of 5 stars I never thought vectors could be so interesting!, June 12, 2000

By 

Matthew Scarpino (Walnut Creek, CA) - See all my reviews

This review is from: A Vector Space Approach to Geometry (Dover Books on Mathematics) (Paperback)

Having suffered through enough dry, pointless courses in vector algebra and analysis, this book was a genuine pleasure. Requiring no mathematical background whatsoever, Mr. Hausner makes the properties of vectors and matrices (cross-products, determinants, eigenvalues) intuitively obvious. With detailed descriptions and graphics, the science of vectors is made very clear. Further, Mr. Hausner's use of levity and practical examples makes for a very enjoyable read.