Things are tricky:
A torus diameter is 4R ! But the torus radius is only R! So its a matter
of perspective.
If you look at the same distance circle radius "torus 2 radii" then the
4D radius - seen in 3D - is longer!
J.W.
On 17.09.2020 23:15, Robin wrote:
In reply to Jürg Wyttenbach's message of Thu, 17 Sep 2020 22:04:39 +0200:
Hi,
You can look up SO(4) in Wikipedia
The group measure is 2^1/2. This is the length of the unit radius of the
Clifford torus (formed by the tangent space). To get the standard norm
(=1) you have to divide by 2^1/2!
Thank you, this now makes sense.
Since 2^1/2 = 1.414... then the 4D radius is larger than the 3D radius, however
previously you wrote:-
"R_4D = 1/2 R_p *(2^1/2 )" , which would make the 4D radius less than the 3D
radius?? (Assuming that R_p is the 3D
radius.) IOW where does the factor of "1/2" come from?
Or more simple. The radius for the standard circle is 1, but the
Clifford torus has two radii, thus its length is (1+1)^1/2
(Pythagoras :- length of the hypotenuse. 4th dimension perpendicular to other
3.)
J.W.
[snip]
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Jürg Wyttenbach
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