Dear Jean-Pierre,

Thank you very much.

> > many thanks for your nice mails about this

> problem.

> > You've probably noticed that when the angle of the

> Simson lines is

> > Pi/3, we get a nice trifolium inscribed in the

> circle(N,R) N = NP-

> center

> > With N as pole and a tangent at a cusp of the

> Steiner deltoid as

> polar

> > axis, the trifolium has polar equation rho =

> R.cos(3.theta)

>

> Some remarks about this trifolium :

> The vertices - contact points with the circle(N,R) -

> are the vertices

> of the equilateral triangle bounded by the Simson

> lines of the

> vertices of the circumnormal triangle; these Simson

> lines are the

> common tangents of the Steiner deltoid and the

> NP-circle at the

> points where they touch each other.

*********

These points are found by drawing from N parallells

to the bisectors of Morley's triangle.

> These vertices

> are homothetic of

> the cusps of the Steiner deltoid in (N,2/3)

> The rectangular circumhyperbola through N intersects

> the circle (N,R)

> at 4 points; one of them is the antipode of N on the

> hyperbola; the

> three other ones are the vertices above.

********

Very interesting.

Happy New Year to you and all Hyacinthists.

Best regards

Nikos Dergiades.

___________________________________________________________

Χρησιμοποιείτε Yahoo!;

Βαρεθήκατε τα ενοχλητικά μηνύματα (spam); Το Yahoo! Mail

διαθέτει την καλύτερη δυνατή προστασία κατά των ενοχλητικών

μηνυμάτων

http://login.yahoo.com/config/mail?.intl=gr