Tesseract: 4D Shape Constructed? Fact or Fiction?

[monty37]

iam sorry if this is crackpottery,but is it true that a 4 dimensional figure*called the tesseract has been constructed,i came across this over the net.*kindly rebuke me if iam not abiding with the rules of pf.

 

[dx]

What do you mean by "constructed"?

 

[Cyosis]

Have a look at http://en.wikipedia.org/wiki/Tesseract it will probably answer all your questions. Assuming with constructed you don't mean built from wood.

 

[monty37]

i mean not exactly constructed,but is the tesseract true,i mean how can a 4d object be
drawn on paper.the link what you gave was where i saw earlier on tesseract,i want
a better explanation.

 

[dx]

The tesseract is not a statement that can be "true" or "false". It's a mathematical object. A 4D object cannot be drawn on paper. The pictures you see of the tesseract are just projections, just like you can project a 3D object onto paper.

 

[monty37]

has the tesseract found its applications in various fields,and on what basis has this been
projected?,i mean considering what as the 4th dimension has this been projected?

 

[Cyosis]

That question was answered in the wikipedia link.

Projections to 2 dimensions

The construction of a hypercube can be imagined the following way:

* 1-dimensional: Two points A and B can be connected to a line, giving a new line segment AB.
* 2-dimensional: Two parallel line segments AB and CD can be connected to become a square, with the corners marked as ABCD.
* 3-dimensional: Two parallel squares ABCD and EFGH can be connected to become a cube, with the corners marked as ABCDEFGH.
* 4-dimensional: Two parallel cubes ABCDEFGH and IJKLMNOP can be connected to become a hypercube, with the corners marked as ABCDEFGHIJKLMNOP.