A Visual Introduction to the Fourth Dimension (Rectangular by Chris McMullen

By Chris McMullen

This colourful, visible creation to the fourth measurement presents a transparent clarification of the thoughts and various illustrations. it's written with a slightly of character that makes this a fascinating learn rather than a dry math textual content. The content material is especially obtainable, but whilst distinct adequate to fulfill the pursuits of complicated readers. This ebook is dedicated to geometry; there are not any religious or spiritual elements to this booklet. could you get pleasure from your trip into the attention-grabbing global of the fourth dimension!

Contents:

  • Introduction
  • Chapter zero: what's a Dimension?
  • Chapter 1: Dimensions 0 and One
  • Chapter 2: the second one Dimension
  • Chapter three: third-dimensional Space
  • Chapter four: A Fourth measurement of Space
  • Chapter five: Tesseracts and Hypercubes
  • Chapter 6: Hypercube Patterns
  • Chapter 7: Planes and Hyperplanes
  • Chapter eight: Tesseracts in Perspective
  • Chapter nine: Rotations in 4D Space
  • Chapter 10: Unfolding a Tesseract
  • Chapter eleven: pass Sections of a Tesseract
  • Chapter 12: dwelling in a 4D House
  • Further Reading
  • Glossary
  • About the Author

Put in your spacesuit, strap in your security harness, swallow your anti-nausea medication, and luxuriate in this trip right into a fourth size of house! 10D, 9D, 8D, 7D, 6D, 5D, 4D, 3D, 2nd, 1D, 0D. Blast off!

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Extra resources for A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry)

Example text

The rays of light that strike your pupil travel in different directions from different parts of the object. You can see this in the previous figure. When you look down a hallway, for example, as illustrated in a couple of the previous pictures, the front square appears larger than the rear square because the rays of light coming from its edges make a wider angle relative to your eye. The illustration below shows a 2D monkey (remember, you have to pin your own tail on the monkey in this book) viewing a tree in perspective.

Every object would look like a line! Did you enjoy contemplating the challenges of designing a 2D world? K. Dewdney. It's a great story where a team of computer scientists discover a 2D universe. It's extremely detailed and very well thought out, and also easy and entertaining to read – it reads like a novel, but is very informative about the second dimension and nicely illustrated. A more popular book on the second dimension, including analogies with 3D and 4D, is Edwin A. Abbott's Flatland. You have to read Flatland if you consider yourself to be a fan of the fourth dimension to any degree.

For example, the planes xy and yz intersect at the y-axis. In 4D space, there are 6 mutually orthogonal planes (remember, they're made out of monkey wallpaper): xy, yz, zw, wx, xz, and yw. The intersection between two of these planes is either a line or a point. When there is a common axis, the intersection is a line (long, straight monkey tail). For example, zw and xz intersect along the z-axis. When there isn't a common axis, the intersection is a single point – the origin, located at (0,0,0,0).

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