# Re: [Vo]:The so-called "secret new weapon"

```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]

```
```--
Jürg Wyttenbach
Bifangstr. 22
8910 Affoltern am Albis

+41 44 760 14 18
+41 79 246 36 06

```