Talk:Soddy's hexlet

Did Dupin know this?
Because of the close relation with the cyclides, it seems plausible that Dupin (or others in the influential French geometry school, such as Darboux) was aware of a similar result in the 19th century, but I don't have a reference. Geometry guy 12:00, 2 March 2007 (UTC)

I've indicated the result which I am almost sure Dupin knew. In fact, this property characterizes Dupin cyclides, but I think this is much later result. I'll dig up the later refs if anyone is interested (seems unlikely for now :) ) Geometry guy 21:55, 20 March 2007 (UTC)

Green spheres?
Where are those green spheres? The figure does not match the text. In this version the description was quite different? --Chricho ∀ (talk) 16:24, 22 November 2012 (UTC)

Calculation of the radii of the spheres of the hexlet from the 3 radii of the initial spheres
Calculation of the radii of the spheres of the hexlet from the 3 radii of the initial spheres

I committed this document: http://mathmj.fr/geogebra/hexlet.pdf which shows that elementary calculations of geometry make it possible to calculate the radii of the 6 spheres of a necklace from the 3 radii of the initial spheres, then To express the links between them. If R is the radius of the bounding sphere, and if a and b are the radii of the first two spheres tangent to each other and tangent internally to the first sphere, it may be remarked in particular that the harmonic means of the radii, areas and volumes of the 6 Spheres of the Necklace are constants dependent only on a, b and R, the standard deviation of the inverses of the rays or of the areas is also constant, but not that of the inverses of the volumes. All these assertions can be verified from the following relationships between the six rays r1, r2, r3, r4, r5, and r6 of the necklace: and we have the relations :

--Majak16 (talk) 09:21, 5 September 2017 (UTC)