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 obtainable, but whilst particular adequate to meet the pursuits of complex readers. This booklet is dedicated to geometry; there are not any non secular or non secular parts to this publication. may perhaps you take pleasure in 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: third-dimensional 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: go 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 measurement of area! 10D, 9D, 8D, 7D, 6D, 5D, 4D, 3D, 2nd, 1D, 0D. Blast off!

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

Sample text

As a simple definition, a dimension is a measure of extent. The dimensions of an object – no, not a plain old object, but a monkey with RAINBOW-colored fur, so this won't read like some boring math textbook – refer to different directions in which an object extends. ), breadth (how wide she is, shoulder to shoulder), and depth (front to back, or nose to tail); she is three-dimensional (3D). However, there are different kinds of dimensions, like space and time – or if you want to get exotic, we can talk about the dimensionality of your thoughts or even your body odor.

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).

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).

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