On Mar 4, 2007, at 11:08 AM, jpehrmfr wrote:

> [Steve]

> > Thanks. I used to call these "polar conics" but Conway has me

> > calling them "diagonal conics." Terminology...ug!

>

> Because they have a diagonal matrix??

Yes, I think this is what they were called when John was at

Cambridge, but it is strange terminology for him has he does not like

geometry terms whose origin is not geometrical.

>

> Let L1,L2 be the infinite points of the diagonal rectangular

> hyperbola h going though M and co the inconic with center M.

> As ABC is selfpolar wrt h and circumsribed in co, P is vertex of a

> triangle inscribed in h and selfpolar wrt co.

> As P is the pole of Linf wrt co, this triangle is necessarily PL1L2;

> which means that PL1, PL2 are conjugate diameters of co. As they are

> perpendicular, they are the axes of co.

Very pretty proof from which I learned a lot

Thanks and best regards,

Steve

Notation:

http://paideiaschool.org/TeacherPages/Steve_Sigur/resources/VoodooPad%

20web/notation.html

Triangle web page:

http://paideiaschool.org/TeacherPages/Steve_Sigur/geometryIndex.htm

Other math:

http://paideiaschool.org/TeacherPages/Steve_Sigur/interesting2.htm

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