+ $3.99 shipping

Arrives: Jan 19 - 25

Fastest delivery: Jan 14 - 20

Only 1 left in stock - order soon.

Ships from	GreenIceMedia
Sold by	GreenIceMedia

Details

Ships from

GreenIceMedia

Sold by

GreenIceMedia

& FREE Shipping

Used: Good | Details

Sold by ThriftBooks-Portland

Other Sellers on Amazon

$34.79
+ Free Shipping

Sold by: BookExcellence

Have one to sell?

Sell on Amazon

Flip to back Flip to front

Listen Playing... Paused You're listening to a sample of the Audible audio edition.
Learn more

See all 2 images

Follow the Author

Thomas Banchoff

Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions (Scientific American Library Series) Paperback – March 1, 1996

by Thomas F. Banchoff (Author)

10 ratings

See all formats and editions Hide other formats and editions

Price

New from

Used from

Hardcover

"Please retry"

$37.08

$29.67

$3.95

Paperback

"Please retry"

$19.90

$9.97

Mass Market Paperback

"Please retry"

—

$72.78

$36.92

This work investigates ways of picturing and understanding dimensions below and above our own. What would a two-dimensional universe be like? How can we even attempt to picture objects of four, five or six dimensions? Such are the questions examined in this text.

Print length

210 pages
Language:

English
Publisher

W H Freeman & Co
Publication date

March 1, 1996
Dimensions

8.75 x 0.5 x 9.5 inches
ISBN-10

0716760150
ISBN-13

978-0716760153
See all details

Customers who viewed this item also viewed

Page 1 of 1 Start overPage 1 of 1

This shopping feature will continue to load items when the Enter key is pressed. In order to navigate out of this carousel please use your heading shortcut key to navigate to the next or previous heading.

Stefan Hildebrandt

6

Hardcover
$19.49
Only 1 left in stock - order soon.
John Archibald Wheeler

27

Hardcover
$49.85
In stock on January 10, 2021.

What other items do customers buy after viewing this item?

Page 1 of 1 Start overPage 1 of 1

Julian Schwinger

4

Hardcover
$31.05
Only 1 left in stock - order soon.
Stefan Hildebrandt

6

Hardcover
$19.49
Only 1 left in stock - order soon.
Keith Devlin

27

Hardcover
35 offers from $20.57

Special offers and product promotions

Amazon Business : For business-only pricing, quantity discounts and FREE Shipping. Register a free business account

Product details

Publisher : W H Freeman & Co; 1st edition (March 1, 1996)
Language: : English
Paperback : 210 pages
ISBN-10 : 0716760150
ISBN-13 : 978-0716760153
Item Weight : 10.6 ounces
Dimensions : 8.75 x 0.5 x 9.5 inches

Best Sellers Rank: #869,684 in Books (See Top 100 in Books)
- #81 in Analytic Geometry (Books)
- #948 in Graphics & Multimedia Programming
- #2,594 in Computer Graphics & Design

Customer Reviews:
10 ratings

Customer reviews

5 star		60%
4 star		28%
3 star		12%
2 star 0% (0%)		0%
1 star 0% (0%)		0%

How are ratings calculated?

Top reviews from the United States

There was a problem filtering reviews right now. Please try again later.

good book

Reviewed in the United States on April 28, 2012

Verified Purchase

I haven't finished yet. But it's really well written. A great book to read as an introduction to hyper-dimensional geometry.

Helpful

Jaime R. Sandoval

Great Book

Reviewed in the United States on December 3, 2008

Verified Purchase

Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions (Scientific American Library Series)

Helpful

Rahman

Concise Well-Written And Beautifully Illustrated Work

Reviewed in the United States on April 22, 2003

Mathematical ideas, when first learned, tend to undergo a curious inner transformation. At the outset, some tangible representation is necessary to effectively latch onto the concept. Thereafter, the symbolic elaboration using the language of mathematics is sufficient to encompass not only that particular figure, but limitless others like it as well. The underlying geometry is still there, but there are simply too many possibilities to illustrate in any amount of time.
The first step of illustrating must be manifest, using ink or chalk or sand or digital pixels. In this way, even the finest geometric illustrations can be considered extremely crude and innacurate in comparison to rigorous mathematical precision. Consider, however, how extraordinarily difficult it would be to grasp trigonometric functions, vector spaces, or even the basic Cartesian coordinate system, without first observing supporting representative illustrations. Even if later forgotten, those initial images are crucial for understanding.
This work provides a wide range of richly color-illustrated examples of the abstract geometric structures dealt with regularly in mathematics and the sciences. It is unique in its quality and affordability, and is supported with excellent prose, briefly describing the developmental history, and frequently how to reconstruct the figures from a sparse handful of assumptions. From an introductory description of dimension, this book then branches into numerous and diverse major topics: scaling, slices, regular polytopes, perspective, coordinate geometry, and non-euclidean geometry. While sparing in its level of mathematical description and precision, it never diverges into a fully artistic exposition on the subjects either. There is a careful balance, to guide the reader into better understanding the particular system under discussion.
Certainly reading this book is merely the first step of a far longer term process. Symbolic computing programs, such as Mathematica, Maple or MatLab, will assist in visualization, as well as in understanding the pragmatic relation between the graphical and set-theoretic descriptions of the figures. Other books will also assist in this. Many of Rucker's works provide further descriptions of certain topics, specifically Geometry Relativity & The Fourth Dimension is admirable in its brevity and profundity. Abbott's classic Flatland is the foundational book on non-technical description of dimensions. The venerable What Is Mathematics? by Courant and Robbins combines illustration and mathematics as well as any work written since. Design science touches on these topics frequently as well, Kappraff's Connections is an extraordinary example of this. Deeper mathematical topics include set theory, algebraic groups, vector analysis, and too many others to list.
However abstract the concepts diagrams and illustrations in this book may seem initially, most if not all have been utilized for practical application in recent times. You may very well be using devices on a daily basis, which have these concepts as a basis for their functionality. Keep this in mind while reveling in what the individual imagination can conjure.

17 people found this helpful

Helpful

Rama Rao

Geometrical Illustrations of Fourth Dimension

Reviewed in the United States on January 28, 2004

Living in a world of three dimensional space makes it hard for us to conceive fourth dimension and it gets even harder to visualize the fifth and higher dimension. Superstring theorists predict the existence of 10th and 26th dimensions in universe; hence it seems reasonable for many of us to understand how it would be like to be living in fourth dimension. Thomas Banchoff is one of the leaders in the study of higher dimension using computer graphics; he has illustrated fourth dimension using basic geometrical approach such as slicing the spatial dimension, observing the shadows of structures, comparing the folded and foldout versions of polytops and description of configuration of spaces. This book is useful for someone who appreciates geometry, but for a reader who likes to visualize the fourth dimension he/she may read Clifford Pickover's Surfing through Hyperspace, which does a better job in illustrating fourth dimension.

8 people found this helpful

Helpful

Helmer Aslaksen

The royal road to geometry!

Reviewed in the United States on February 26, 2001

This book is a jewel! It contains a wide collection of visual geometry. Professor Banchoff is able to link geometry to many aspects of life. It's a treasure trove for anybody teaching geometry at any level. It's a book that can be read at many levels. If you're willing to skip a bit here and there, you can get a very good general idea. But if you want to really understand all the details, it can make for hours of challenging reading. I'm still reading it! :-)

9 people found this helpful

Helpful

Didier Bizzarri (D.Bizzarri@ulg.ac.be)

A must reading for any geometry enthusiast!

Reviewed in the United States on November 30, 1998

After reading this book, no doubt Thomas Banchoff is a deeply experienced geometry enthusiast.Unlike many schoolbooks, his book shows the main ideas underlying a multi-faceted geometry with minimal technical complication nonsense, using simple concepts and a bright argumentation, almost without losing insight! He never misses an opportunity to connect geometry to other sciences like algebra, relativity, optics, mechanics and to arts. It is not only the 'Everything you desired to know about the 4th dimensions' but also a bunch of 2D and 3D geometry 'master tricks' as well as a historical narration (including recent discoveries).
Examples: - how to find yourself the polytopes (4D 'polyhedra') with 3D representations - how to easily calculate vertex coordinates of the 5 polyhedra - how to draw a torus on a hypersphère! -.. and many others
No way you could escape this reading with the same vision of geometry!

27 people found this helpful

Helpful

Howard Schneider

What is a dimension?

Reviewed in the United States on November 25, 2000

A comfortable introduction to modern geometry for the general reader, with emphasis on the concept of the dimension. This reference concludes with an introduction to non-euclidean geometry.

3 people found this helpful

Helpful

P. R. Bialek

Very good intro to the 4th dimension

Reviewed in the United States on October 27, 2013

This is an excellent introduction to the 4th dimension (and the 5th). It's a little difficult to follow in places, but in general readable and interesting. I will definitely use this as a resource when I teach college-level geometry courses.

Helpful

Pages with related products. See and discover other items: analytic geometry

Other Sellers on Amazon

Follow the Author

Similar authors to follow

Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions (Scientific American Library Series) Paperback – March 1, 1996

Customers who viewed this item also viewed

What other items do customers buy after viewing this item?

Special offers and product promotions

Product details

Customer reviews

Top reviews from the United States

There was a problem filtering reviews right now. Please try again later.

Top reviews from other countries

Buy used: $9.97

Other Sellers on Amazon

Follow the Author

Similar authors to follow

Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions (Scientific American Library Series) Paperback – March 1, 1996

Customers who viewed this item also viewed

What other items do customers buy after viewing this item?

Special offers and product promotions

Product details

Customer reviews

Top reviews from the United States

There was a problem filtering reviews right now. Please try again later.

Top reviews from other countries

Buy used:

$9.97