/sci/ - Science & Math

>>9413041
Tried your method but still can't visualize a 3-sphere in my head

>>6656061
It's not just hard to draw, It's impossible to draw the hole thing. However you can draw projections. Drawing the complete brane witll require a 4th spacial dimension. But it is easy to mathematically conceptualizes.

I'll use the n-sphere as an explict example:
The 1-sphere (unit circle) can be mapped by the following function <span class="math"> \sigma_1 : \mathbb{R} \rightarrow \mathbb{R}^2 [/spoiler] that take all points form 0 to 2<span class="math">\pi[/spoiler] to the unit circle.
<span class="math"> \sigma_1 (\theta) = (cos(\theta), sin(\theta) ) [/spoiler]

The 2-sphere uses <span class="math"> \sigma_2 : \mathbb{R}^2 \rightarrow \mathbb{R}^3 [/spoiler]
and can be defined by:
<span class="math"> \sigma_2 (\theta,\phi) = (sin(\phi)cos(\theta), sin(\phi)sin(\theta), cos(\phi) ) [/spoiler]

...and the 3-sphere (a closed 3 brane) can be difined by <span class="math"> \sigma_3 : \mathbb{R}^3 \rightarrow \mathbb{R}^4 [/spoiler] :

<span class="math"> \sigma_2 (\theta,\phi,\psi) = (sin(\psi)sin(\phi)cos(\theta), sin(\psi)sin(\phi)sin(\theta), sin(\psi)cos(\phi), cos(\psi) ) [/spoiler]

Does anyone know how to visualize a 4-D sphere? What about a 5-D sphere?

I have trouble making sense of these higher dimensions. I'd really like to understand how to visualize a 3-D shape in 4-D or a 2-D shape in 4-D.

Anyone have some ideas???

How do you project 4dim sphere into a 2d plane ?

heres a 4 dimensional sphere

http://www.blazelabs.com/
Has anyone with credibility ever critiqued this website? If so, how much would you say is bs and how much is plausible.
picture loosely related.

Hey /Sci/

I was playing around with N-dimensional geometry and something occurred to me,

What if c is the lower bound of the hyper-velocity of matter and all matter was essentially tachyonic?

Time is not a fourth Euclidean dimension. When people talk about the "Fourth dimension" and doing 4th dimensional geometry [re: tesseracts and junk], they mean the Euclidean dimension of the w axis, not time.

If Time is to be considered a dimension, we'd be better off calling them the Three Spatial Dimensions and the First Temporal Dimension.

hypersphere?

here is the equatorial view of a 4d sphere. the 3 equatorial circumference are represented as green red and blue