By Chris McMullen
This colourful, visible advent to the fourth size offers a transparent clarification of the innovations and various illustrations. it really is written with a slightly of character that makes this an enticing learn rather than a dry math textual content. The content material is especially available, but even as specific adequate to fulfill the pursuits of complex readers. This e-book is dedicated to geometry; there aren't any non secular or non secular parts to this publication. may possibly you get pleasure from your trip into the interesting global of the fourth dimension!
- 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: pass Sections of a Tesseract
- Chapter 12: dwelling in a 4D House
- Further Reading
- About the Author
Put in your spacesuit, strap in your security harness, swallow your anti-nausea drugs, and revel in this trip right into a fourth size of area! 10D, 9D, 8D, 7D, 6D, 5D, 4D, 3D, second, 1D, 0D. Blast off!
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Additional resources for A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry)
Just imagine 100 students enrolling for a course, where only ten of them actually expect to do theoretical physics. As fascinating as the subject is, we're not going to discuss (any more) string theory in this book. I know; make a sad face. The focus of this book is on the geometry of a fourth dimension of space that is very much like the usual three dimensions. We're also not going to talk about compact dimensions (any further). Click here to return to the Table of Contents. Otherwise, keep reading.
This is illustrated in the figure below. If you multiply this by 16 corners, you get 6 x 16 = 96. But the answer is not 96 because we have counted each square too many times. We actually counted each square 4 times because each square connects to 4 corners. So the formula for the number of squares in a tesseract (full of monkeys) is 6 times 16 divided by 4 = 24. The 6 is how many squares meet at each corner; there are 16 corners; and we divide by 4 because each square has 4 corners (so 6 x 16 counts each square 4 times; dividing by 4 corrects for over-counting).
A 2D monkey living in a 2D world wouldn't have eyes inside his head, though. Even walking would be much different: A 2D monkey can't put one foot in front of the other; the same foot would always be in front. ) Unlike the first dimension, 2D beings can pass their nearest neighbors. But unlike 3D, they can't pass around them – they must pass over or under. Just imagine the guy in the front row of a crowded movie theatre going out for some popcorn: He's not going to be the most popular fellow!
A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry) by Chris McMullen