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]