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Geometry

Spacial Dimensions - What is the Fourth Dimension? - What are the Tesseracts & the HyperCubes?

Unfolding the HyperCube - 3d-Puzzle - Digital Books


Geometry

Geometry (from the Ancient Greek: (γεωμετρία); geo - “earth”, -metron “measurement”) is a branch of Mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

In Mathematics and Physics, the dimensions of a space or object are informally defined in Euclidian Geometry as the minimum number of coordinates needed to specify any point within it.

3D2D Geometry

The 3D2D Geometry Website describes the 2-Dimensional Shapes and 3-Dimensional Objects,
and illustrates dynamically the way they intersect with the plane or between themselves.

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Spacial Dimensions

Spacial Dimensions


Geometric Objects in higher Dimensions can be unfolded in lower Dimensions.

Spacial Dimensions


Although human beings only have immediate experience of the 3-Dimensional Space, this does not rule out at all the existence of other higher-numbered ones called Hyper-Spaces, the 4-Dimensional Space being one of them. They are therefore an infinity of higher dimensions.

Advanced physics such as String Theory considers higher dimensions. The Super-string Theory and M-Theory suggest that physical Space has ten and eleven dimensions, respectively. These extra dimensions are said to be spatial. However, we perceive only our 3-Dimension Space. A possible explanation that has been suggested is that Space acts as if it were “curled up” in the extra dimensions on a subatomic scale, possibly at the quark/string level of scale or below.


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What is the Fourth Dimension?

The Fourth Dimension or 4D is NOT TIME, but space. Not outer space, but another spatial direction which extends in a direction perpendicular to all directions we are used to know in our Three Dimension or 3d Space or Universe.


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What are the Tesseracts & the HyperCubes?

in Euclidean Geometry, HyperCubes are cubes in a Space of more than three dimensions. In a four dimensional Space the hypercube has a special name. It is called a Tesseract or 8-Cell. They consist of a cubic honeycomb that has 4 cubes around every edge, and 8 cubes around each vertex.

Graph of a Tesseract in the 3d Space

Tesseract

A 3D Projection of Tesseract
performing a double rotation

Moving Tesseract


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Unfolding the HyperCube

Unfolding a 4D-Cube and a 3d-Cube

HyperCube Unfolding

Illustration of Dimensions 1 to 4

1D to 4D animation

Unfolding the HyperCube


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3d-Puzzle

The 3d-Puzzle is made of eight Cubes with articulations to simulate the unfolding of a HyperCube or Tesseract from the 4-Dimension to a 3d-Cross in the 3-Dimension Space.

8 Cube Puzzle & Solution



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Digital Books

The Digital Books review in detail the 1, 2, 3 and 4-Dimension Spaces, their relation, how it is possible to go back and forth between the 2 Spaces, and more.

The Dimensional Spaces have been identified as:

Dimensions

Click here for more details

Available in the ONLINE STORE