Read e-book online A Visual Introduction to the Fourth Dimension (Rectangular PDF

By Chris McMullen

This colourful, visible advent to the fourth size presents a transparent rationalization of the options and diverse illustrations. it's written with a marginally of character that makes this an attractive learn rather than a dry math textual content. The content material is especially available, but even as unique adequate to meet the pursuits of complicated readers. This publication is dedicated to geometry; there aren't any non secular or non secular elements to this publication. may possibly you take pleasure in your trip into the interesting 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: three-d Space
  • Chapter four: A Fourth size 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: residing in a 4D House
  • Further Reading
  • Glossary
  • About the Author

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

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

Sample text

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. Trying to draw the third dimension on a plane creates some ambiguity, such as the one illustrated below. You can interpret the red, blue, and green cube below two different ways: You can picture it with the corner C in the front or the back. When you imagine that C is in the front, you picture a cube extending up and to the right; but if you imagine that C is in the back, you picture a cube extending down and to the left (as if you're inside a room looking at a corner on the floor).

There's a major problem: You can't use an axle to join the wheels together! The wheels of a 3D car have a rod that connects them; the rod is perpendicular to each wheel. In 2D, you can't make the axle perpendicular to the wheels, since they must all lie within the same plane. Maybe 2D monkeys could stand on top of the wheels and roll them like loggers. Another simple machine that would be different is the pulley. In 3D, pulleys also involve a wheel-and-axle design. Nonetheless, it would be possible to make a pulley in 2D without an axle: The wheel could simply sit in a cradle, using a lubricant to prevent it from rolling out with friction.

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. It's not quite as easy reading for math and science lovers, as it's not just a work of geometry and philosophy, but is also a literary work written in 1884 with themes regarding Victorian times.

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A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry) by Chris McMullen


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