Subject: Re: [HM] L'Hopital, Pythagoras, Ptolemy and Hilbert
From: Floor van Lamoen (f.v.lamoen@wxs.nl)
Date: Mon Mar 20 2000 - 07:53:51 EST
Antreas P. Hatzipolakis wrote:
> Andrew Bowering wrote (in part):
>
> > I am in my final year of a degree course in Mathematics and in need of
> > big help. I have noticed the wealth of knowledge out there amongst
> > you but now I need to tap into this knowledge. Firstly I need some
> > examples of results which are not named after the people who derived
> > them - ie - L'Hopital's rule, found by his tutor Johann Bernoulli.
>
> Dear Andrew,
>
> Following are a few examples from Euclidean Geometry:
>
> 1. Apollonian Circle:
>
> This circle as locus-proposition appeared first in Aristotle, Meteor. III.
> 5.375b16 - 376b12
>
> Reference:
> Thomas Heath: Mathematics in Aristotle.
> Bristol: Thoemmes Press, 1998, pp. 181ff.
>
> 2. On the Lemoine Point a.k.a. Grebe Point:
>
> See the HM thred "Grebe":
>
> http://forum.swarthmore.edu/epigone/historia_matematica/phelchosneh/
>
> 3. On the Feuerbach Circle a.k.a. Euler Circle:
>
> See the HM thread "Benjamin Bevan's Problem":
>
> http://forum.swarthmore.edu/epigone/historia_matematica/foxkhowhil
>
> Good Luck!
>
> Antreas
In addition:
4. The Schiffler point: the point of concurrence in triangle ABC with
incenter I of the Euler lines of triangles ABC, ABI, AIC and IBC.
The point is named after a problem proposed by Kurt Schiffler in Crux
Mathematicorum:
Problem 1018 and solution, Crux Mathematicorum 12 (1986) 150-152
[proposed 1985].
The fact that the incenter I was on the locus of points X such that ABC,
ABX, AXC and XBC was already published in:
F. Morley and F.V. Morley, Inversive Geometry, Chelsea Publ. Co., New
York (1954),
in which it is an exercise to show that the locus is the union of the
famous Neuberg cubic (containing I) and the circumcircle of ABC.
Kind regards,
Floor van Lamoen.
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