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Beyond The Third Dimension: Geometry, Computer Graphics, And Higher Dimensions

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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.


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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.

51 review for Beyond The Third Dimension: Geometry, Computer Graphics, And Higher Dimensions

  1. 4 out of 5

    Madeleine Morales

    great graphics, useful diagrams, and a wonderful explanation of the hypercube

  2. 4 out of 5

    Rama

    Geometrical Illustrations of Fourth Dimension 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; Geometrical Illustrations of Fourth Dimension 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.

  3. 4 out of 5

    Paul Bialek

    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.

  4. 4 out of 5

    Kazuo

    A nice and very accessible introduction to higher dimensions. There are plenty of computer-generated graphics to feed the intuition, and I particularly liked a section on representing sets of data in more than three dimensions.

  5. 4 out of 5

    Kenneth

    A fascinating layman's review of geometry in higher dimensions

  6. 5 out of 5

    Donizetti Louro

  7. 5 out of 5

    b1n0ry

  8. 4 out of 5

    Dave

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    Paul Vittay

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    Kara

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    Quinn

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    Izak Botha

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    Steve

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    Günther Leenaert

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    Andrea De Domenico

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    Carlos Ponce

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    M.E. Hogan

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    Ahmed Ibraheem

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    Greg Friedman

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    Joa Chilltinbarca

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    Michael A. Sherbon

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    Nelson Lama

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    JustinL42

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    Bob Day

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    Dan Schapiro

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    libreriacosimoave

  40. 5 out of 5

    Aristoteles Antonio

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    MBB

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    Robert

  50. 5 out of 5

    Andrew Kinard

  51. 4 out of 5

    Joelle

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