Dear members, I am pleased to be a recent member of your excellent and well-named group. I have recently discovered a solution to Apollonius' problem of...
Dear all, Steve Sigur and Bernard Gibert have brought forward some properties of Kiepert's hyperbola: 1. Isogonal conjugates of Brocard line OK 2. Isotomic...
... Perhaps I can preserve your next copy of the NYTimes. Here are the results of some messy calculations. Of course, the computer did all the messy work, but...
... Dear Antreas, Sorry, I don't know the author of your problem and it is not in Collet & Griso unless I did not see it ! This book is a real gold-mine...
Dear Antreas and all, ... there is a whole book to write about this stuff and I just want to make a few comments : 1). this cubic belongs to a family of...
... Dear Bernard I have a question about a locus which probably is included in the book above, a book which I heve not seen: Who is the author of this problem...
... The conjecture was: Let ABC be a triangle. From A we draw parallels to b- and c- altitudes intersecting the BC at Ba, Ca respectively. Similarly, we define...
Dear Steve and friends, I have found a quite different approach to the Fermats,etc based on projective geometry : Let's call (F) the pencil (faisceau in...
... Dear Bernard, Neither I am, but JHC has already provided one. This message is about another coordinates Floor once used, namely Bottema's r-coordinates. ...
... It is the circle with diameter GH. Cf.: Cercle orthocentroidal (TUCKER). Cercle decrit sur GH pris pour diametre. Voir _Mathesis_, 1890, p. 166, et 1893,...
The coordinates x,y,z being proportional to the perpendicular distances from the sides of a triangle ABC, prove that (1) the locus of a point (x,y,z) such that...
... Jacques Gabay Editions: Les Editions Jacques Gabay sont specialisees dans la reedition de grands textes scientifiques concernant principalement les...
Dear Antreas and all, ... Those coordinates are called "tripolar coordinates" by Trajan Lalesco (la géométrie du triangle, p.28. excellent small book written...
HAPPY 2000, FRIENDS ! Feuerbach Theorem: The nine-point circle touches the incircle and the excircles at, say, Fo, F_a, F_b, F_c. ? Theorem: The lines AF_a,...
here is a small poem written by a good friend of mine : Le point rose regarde la droite bleue Dans les yeux La droite bleue caresse le cercle rouge cru Sans...
Steve, thank you for your nice message. ... What a good piece of news ! Do not hesitate to correct my English when I misuse some geometrical denominations ... ...
... John, the title of the copy that I have reads: Exercices de geometrie comprenant des methodes geometriques et 2000 questions resolus. Par F.G.-M. Cinquieme...
Dear Antreas, ... Those two points are called 1st and 2nd Schröter points : they both lie on the 9pt circle. (Schröter 1865) They have quite a lot of...
... The term "desmic" ("desmique", in fact) was introduced by the mathematician C. Stephanos. Although one may suspect that the Greek word working here is...
Le lieu des sommets des rectangles circonscrits a une ellipse donnee est un cercle concentrique a cette ellipse. Le lieu du sommet d'un angle droit circonscrit...
I am FWDing to the list the following message by John Conway for those who are not members in geometry-forum. (In the end I add a problem). ... Date: Wed, 29...
Dear Antreas, ... As far as I can tell, he lived in France. ... Not quite. If you really are interested in, I think it is possible to find out more on Frère...
... H. S. M. Coxeter: Given six consecutive points A, B, C, D, E and F on a circle, prove that if (AB)(CD)(EF) = (BC)(DE)(FA), then AD, BE and CF are...
Dear triangle geometers, I'm sure I speak for many who thank Antreas for establishing Hyacinthos@onelist. Antreas mentioned that that name Hyacinthos honors E....
Dear Friends, Seasonal Greetings from Athens. And Happy Birthday, John! Following are some theorems / conjectures on what I call "orthial triangles". Let ABC...
<quote> A visual homage to Alberto P. Calderon Miguel de Guzman Garcia-Monge - Miguel de Guzman Ozamiz Madrid, December 1998 A solution to the Apollonius...
X_76 [in Clark Kimberling's _TCCT_]: [Name]: 3rd Brocard Point. [Trilinears]: (:b^(-3):) [Geometrical Properties]: The Brocard midpoint (X_39) of the ...
Hello friends and season's greetings, This note is to comment on the connection between the Kiepert hyperbola, the Euler line, the Brocard line, and the four...
As an interesting final posting about the Fermats, I will compute the points where the lines FnFs and NnNs cross the Euler line. The notation is explained in...
Dear Steve, Steve Sigur wrote on the Fermat et al. points: <...> ... <...> ... <...> ... <...> ... <...> It is no coincidence that points on the Euler line are...
