Tesseract Challange

[keeperx]

no, i get it.. the tesseract i posted was from a DXF file and laserboy did the blanking..

I understand the tesseract, and have for a long time.. thats why i started the challenge..

For the sake of this challenge, im just looking for a 3d representation of a tesseract, after all ilda is ONLY 3d and has no 4th dimension to draw in.

so by creating the 3d shadow of a rotating tesseract in ilda space, you are achieving the absolute most that is possible as far as this challenge, and any 3d drawing tool, and the ILDA file format are concerned.

Im not being holier than anyone.. im just trying to include lots of links and information for people to view that may help them.

That carl sagan video has been around forever, i watched the entire cosmos series years ago, that guy was out there with some of his thinking.. he was also an advocate for legalization of marijuana.

here is an easy question..

what is the volume of a tesseract with dimensions of
x=5
y=5
z=5
h=5

[-bart-]

A tesseract has no 'volume', just like a cube has no length, you could say that the 3d-shadow of a tesseract has a volume of 125m^3.
You might even say that is has a squared surface of 625m^4.

[Zoof]

Assuming that you were asking for the 3D volume it is 5^3 * 8 = 1000;
I'll admit that it took a while to see that one.
The 8 cubes are: 6 on each face of the inside cube plus the inner and outer cubes.
By watching the animated rotation you can see why the latter count as well.

p.s. there are tons more of interesting math puzzles on the web

[Zoof]

A tesseract has no 'volume', just like a cube has no length, you could say that the 3d-shadow of a tesseract has a volume of 125m^3.
You might even say that is has a squared surface of 625m^4.

the volume to a tesseract is like the surface of a cube. It is one dimension less.
For a 3D cube's surface you count the number of surfaces and multiply by their surface measure.
For a 4D tesseract's volume you count the number of cubes times their volume.

[keeperx]

the volume of a cube is is (length of side)^3
the tesseract would be (length of side)^4

edit.. zoof beat me to it.. but yes.. a cube does have volume..

[Zoof]

the volume of a cube is is (length of side)^3
the tesseract would be (length of side)^4

edit.. zoof beat me to it.. but yes.. a cube does have volume..

Silly me, I thought you were asking for the 3D volume - it wasn't easy so should have known you meant 4D volume.

But what is the proper term for `4D volume' ?

[keeperx]

i would think that it would be hypervolume

[Zoof]

i would think that it would be hypervolume

right so the volume of a tesseract is L^3 * 8, is 1000 for L=5,
and the hypervolume is L^4, is 625 for L=5.

[keeperx]

ooo tricky.. good answer...
way to nail me on semantics..


I was thinking of building a 3d version of the hypercube. i have an idea how to do it with dowels that slide into tubes so the sides can get bigger and smaller


edit--
i also think that a hypercube does NOT have volume as it cant exist in 3d space, only its "shadow" has volume so you use normal 3d volume for the calculation

[Zoof]

edit--
i also think that a hypercube does NOT have volume as it cant exist in 3d space, only its "shadow" has volume so you use normal 3d volume for the calculation

See this is what I mean by 'learning from youtube'.

The imagination can't grasp 4D, that is why we have mathematics.

Just like a cube has a surface (one dimension less), a hypercube has a volume (also one dimension less)

Looking at a 2D projection of a cube, the parallelograms represent square surfaces in the original 3D world.
Looking at a 3D projection of a hypercube, the skewed cubes represent the cubic volumes of the hypercube in the original 4D world.

I'll let the discussion rest. Interesting topic. Now I know enough to implement it. I won't post here until I have proof