By Chris McMullen

This colourful, visible creation to the fourth measurement presents a transparent rationalization of the recommendations 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 particularly available, but whilst distinct sufficient to fulfill the pursuits of complex readers. This e-book is dedicated to geometry; there aren't any religious or spiritual parts to this ebook. could you take pleasure in your trip into the attention-grabbing 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: 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 drugs, 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!**

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

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

**Sample text**

The many resulting colors have to do with transparency (you can see "through" the faces partially, so the colors that you see are a combination of 2 or more planes). In the next figure, each hyperplane is a solid color. The colors are much more straightforward this time, if not quite as pretty. There are 6 different ways that 2 of the 4 hyperplanes can intersect. In each case, the region of intersection is a plane. This is shown in the following picture. Now let's consider how planes, hyperplanes, and their intersections relate to the structure of the cube and tesseract.

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). The two bottom figures show how both possibilities can be constructed by folding the L-shape two different ways. Mathematically, we can graph 3D using a coordinate system. If you stand in the corner of a room and look at the corner on the floor, this can help you to visualize a 3D coordinate system, with x-, y-, and z-axes.

This is exemplified in the following figure, which shows three different sets of coordinates that result in a point lying at the same position in the sheet of paper. Although there is a little ambiguity in drawing 3D objects on 2D paper, there is even more ambiguity in drawing 4D objects on a 2D paper; and to make matters worse, we don't have experience living in 4D space. Nonetheless, we can still learn a lot about the geometry of the fourth dimension. In this book, we will approach this from a conceptual standpoint, but keep in mind that it is straightforward to work out the algebra for the fourth dimension.