Exploring the Fourth Dimension Quiz

Answer: Euclidean

If we were speaking of time-space, the answer would be Minkowski space. Spatial dimensions are different from space-time theory.
Our third dimension is composed of length, width, and depth. The fourth dimension is believed to have another inexplicable dimension. There are therefore FOUR dimensions.

Answer: Tesseract

A hypercube is a figure used to describe the space in other dimensions. The hyperspace in the fourth dimension is impossible to describe due to the limitations of our own dimensions. The fourth dimension can only be understood as an abstract.

Answer: Charles Hinton

Charles Hinton (1853 - 1907) coined the term "tesseract" in the Dublin University magazine in 1880. Hinton was a British mathematician who also wrote science fiction pieces.

Answer: "Flatland: A Romance of Many Dimensions"

Flatland was written in 1884. It is about a two dimensional world in which men are polygons and women are line segments. The narrator, A. Square, is then visited by a three dimensional sphere but does not understand it due to his dimensional limitations.
Since then, numerous imitations have been created including "Sphereland" by Dionys Burger.

Answer: 2(π^2)(r^3)

Most people tend to use an incorrect formula. This is because they usually add or multiply the formulas for circumference (2πr) and surface area (4π(r^2)) improperly. The accepted formula for the surface volume of a fourth dimension hypersphere (2(π^2)(r^3)) has been rigorously tested.

Answer: Yes

Special relativity is generally the theory of measurement in inertial frames of reference. Special relativity has also been extended to spacetime. The equations of fourth dimension spacetime are written in Lorentz covariant form. The four variables used are (ct, x, y, z).

Answer: Polygraphic projection

Polygraphic projection is not a demonstration of a hypercube.
The Schlegel and Hasse diagrams are both 2D representations. The Stereographic projection has 3rd dimension edges. Diagrams can be seen here:

Schlegel: http://wpcontent.answers.com/wikipedia/commons/thumb/a/a2/Schlegel_wireframe_8-cell.png/240px-Schlegel_wireframe_8-cell.png

Hasse: http://farm3.static.flickr.com/2025/2254800793_6fde4a7587_m.jpg

Stereographic: http://math.ucr.edu/home/baez/Stereographic_polytope_8cell.png

Answer: ana/ kata

In the third dimension, we have the limitations of up/down, left/right, and forwards backwards. In the fourth dimension, the directions of ana/kata are added. Note: these are attested terms. They cannot be taken formally.

Answer: False

It will cast a third dimension shadow. A parallel example to this is how a third dimension object will cast a second dimension shadow. This is due to the lighting phenomenon which exists differently in other dimensions.

Answer: True

Spacetime is shown by the variable ct. Because of the fusion between space and time, one can therefore say that in the fourth dimension, you can theoretically walk through walls, be in two places at once, and move into a new type of space not otherwise possible. We have mathematics and quantum physics to thank for all of this.