Re: [EMHL] Parallel tripolars
- Dear Antreas and Steve,
>> Steve wrote:This is only a special case of the more general theorem :
>>> Mineur ---
>>> The 12 point cubic (isogonic with pivot K) is the locus of inverse points
>>> whose axes of perspective are parallel.
If W (p,q,r) is the pole of the isoconjugation
P(x,y,z) ----> P'(p/x,q/y,r/z),
then the locus of P such that the tripolars of P and P' are parallel is the
pivotal cubic with pivot W i.e. pole = pivot !
Equation (barys) : px(ry^2 - qz^2) + cyclic = 0.
When W = K, you have the isogonality with the 12 point cubic.
When W = G, you have the isotomy with the union of the 3 medians.
Remark : there is only one circular such cubic for W = X67 (isotomic of the
Droussent pivot X316).