Hypersphere 2

Stereographic projection of the "toroidal parallels" of a hypersphere.

[W-INTERNATIONAL-SYNDICATION]

I don't know what the hell I just watched but it's absolutely beautiful.

[SaldithLP]

@Tony Burk: I dont think that this is a rotation, but a hypersphere crossing through the 3rd dimension!

[kmylodarkstar]

this is the real universe, we think is expanding but there is no time, is just a perception of an object with many dimensions of a higher magnitude.

[rareaudiobooks_]

What would music look like in hyperspace? The illusion of a repeating pattern in the hypersphere reminds me of a sin wave or something like sound emanating from a speaker. Or the effects of convolution reverb tails which imply space mathematically, but only exist as sound waves.

[yun.mp]

I love this, so cool to try and visualise what a hyper sphere might look like!

Just a shame we can only see it from our 3D perspective it’s always boggled my mind how a 4D object would use time as a dimension or depth as a surface dimension is crazy.

[quasistarsupernova]

fun project (multivar calc students) use quadruple integrals to try to find the volume of a hypersphere in the 4th dimension. First start with 2d with double integrals, than 3d with triple integrals and then move on to 4d with quadruple integrals, (it's fun, trust me)

[charlieherman]

THOROUGH EXPLANATION: This doesn't quite look like a hypersphere, this looks more like a hypertorus. Instead of visualizing a single slice that would result from a 4d object passed through the 3d "plane, " we're seeing the level surfaces of the 4d hypertorus.
Think of a 2d curve where y is a function of x:= y=f(x). Example: y=sinx [sine curve]; as you move along the x-axis the 1d DOTmoves up and down in the y direction.
One dimension up, and we have a 3d surface where z is a function of x and y:= z=f(x, y). Example: z=x^2+y^2 [sphere]; As you move along the z-axis, the 2d circle (CURVE) changes in the x, and y directions getting bigger and smaller.
In this case, the hypertorus is a function of x, y, and z such that w=f(x, y, z). As we move along the "w" axis the 2d CURVE changes in the x-y-z plane. If the equation of a torus is written such that z=f(x, y), then z^2=a^2-(c-sqrt(x^2+y^2))^2. As you move along the z-axis you see two concentric rings getting bigger and smaller in the x and y directions.
Up one more dimension to the hypertorus, and you have w is a function of x, y, and z such that w=f(x, y, z). If a 4d hypertorus was to move through a 3d environment along the w-axis, the 3d SURFACE would change in the x, y, and z directions. As we move along the w-axis, we would see what looks like a small thin torus growing in thickness, turn inside out briefly as the "inside" and "outside" switch, then the torus would get thinner until nothing.
Instead, my theory is that this is a hypertorus with its z-axis at an angle to offset the symmetry, and instead of seeing a single "slice" of the 4d shape we are seeing a 3d projection of the level surfaces, but instead of viewing all of the level surfaces at the same time (impossible for a 3d being) we move along the w-axis encountering various level surfaces that change shape due to our motion. In reality, all of these level surfaces are stacked along the w-axis and the 4d shape is comprised of all of those shapes at the same time.

[Dafuqno.]

So. It bends, turns on in of itself, and manages to collapse out of

[rainyhi]

It’s a 4d object in a 3d plane on a 2d screen.

[cloud__zero]

Wouldn't a hypersphere be a sphere evolving over time ?
Or are we talking about geometrical 4D ?

[Hxr]

I don't suppose you could tell me what the equations were you used to do the rotation?

[allertonoff]

hi, this is _Great, _ may i borrow it for an unfunded experimental video ?

[FcLover]

I think what you're seeing here is an example of what it will look like if a hypersphere aka a 4 dimensional sphere would look like if it passed our world, but don't believe in me it's just my opinion