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

By Chris McMullen

This colourful, visible creation to the fourth size offers a transparent clarification of the thoughts and various illustrations. it truly is written with a slightly of character that makes this an interesting learn rather than a dry math textual content. The content material is particularly available, but even as specific sufficient to meet the pursuits of complicated readers. This publication is dedicated to geometry; there are not any non secular or spiritual elements to this publication. may possibly you get pleasure from your trip into the interesting international 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: three-d 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: move 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 revel in this trip right into a fourth measurement of house! 10D, 9D, 8D, 7D, 6D, 5D, 4D, 3D, second, 1D, 0D. Blast off!

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Additional info for A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry)

Sample text

If you look at one edge of a tesseract (filled with howling monkeys – you'd howl too, if you were trapped in a tesseract), you should be able to find 3 squares meeting at that edge. This is shown in the figure below. Recall that there are 32 edges in a tesseract. 3 squares times 32 edges makes 96 squares, then we divide by 4 to correct for quadruple counting (since there are 4 edges in each square). 3 x 32 / 4 = 24, which agrees with our previous solutions. Puzzle #4: If you place a monkey inside every cube of a tesseract, how many monkeys will there be?

Establishing the basic laws of physics in order to try to design a 1D world that mimics some features of our universe, that's where the challenge is. For example, if you want matter to be made up of "atoms," how do you propose to make orbits in a 1D universe? One object can't go around another (unless you want to be really creative and allow a particle to make an "orbit" by traveling through wormholes, like the hypothetical hyperspace orbit figure that follows). A back-and-forth motion would be more natural than an orbit.

Still, good luck. With that in mind, you can appreciate our challenge in trying to understand the fourth dimension. It's easier for us though: The leap from 3D to 4D is easier to grasp than the leap from 2D to 3D would be. In the following figure, the 2D being (tail-less monkey, of course) is contemplating a third dimension of space. We ourselves have a few difficulties visualizing the third dimension, and we live in it! We see a 2D image of 3D objects with our eyes, and we draw 2D representations of the third dimension on paper.

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Categories: Geometry Topology