By Chris McMullen

This colourful, visible creation to the fourth measurement presents a transparent clarification of the thoughts and various illustrations. it truly is written with a marginally of character that makes this an enticing learn rather than a dry math textual content. The content material is particularly available, but while particular adequate to meet the pursuits of complicated readers. This publication is dedicated to geometry; there aren't any non secular or spiritual parts to this e-book. might 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: 3-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: residing in a 4D House
- Further Reading
- Glossary
- About the Author

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

**Read Online or Download A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry) PDF**

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

**Sample text**

Now let's consider how planes, hyperplanes, and their intersections relate to the structure of the cube and tesseract. The cube is bounded by 6 squares (which are planar). Two adjacent square faces intersect at a line (each edge). The 12 edges (monkey tails) are the regions where two square faces intersect. The cube is bounded by 6 square faces, which are joined together at 12 edges. Similarly, the tesseract is bounded by 8 cubes (which are hyperplanar). Two adjacent cubes intersect at a square (which is planar) in 4D.

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).

Two adjacent square faces intersect at a line (each edge). The 12 edges (monkey tails) are the regions where two square faces intersect. The cube is bounded by 6 square faces, which are joined together at 12 edges. Similarly, the tesseract is bounded by 8 cubes (which are hyperplanar). Two adjacent cubes intersect at a square (which is planar) in 4D. ) The 24 squares are the regions where two cubes intersect. The tesseract is bounded by 8 cubes, which are joined together at 24 squares. Click here to return to the Table of Contents.