Antreas: Many thanks for your note on Soddy circles. I see now that their centres (a +/- ra::) are Clark Kimberling's X176, X175. It is intriguing that ...
834
xpolakis@...
May 1, 2000 5:33 pm
... You are welcome, Dick. ... Coxeter - Greitzer (Geometry Revisited, p. 114, Exercise #4) write parenthetically: "(They are sometimes called Soddy's circles...
835
xpolakis@...
May 1, 2000 6:54 pm
... Dear Paul, This schema has more interesting properties. A /\ / \ / \ / \ / \ Cc Bb /q q\ / A* \ /...
836
Ignacio Larrosa Ca...
ilarrosa@...
May 1, 2000 10:17 pm
... From: Dick Tahta To: Hyacinthos@egroups.com Cc: Hyacinthos@egroups.com Sent: Monday, May 01, 2000 2:45 PM Subject: Re: [EMHL] Lemoine query Antreas: Many...
837
Steve Sigur
ssigur@...
May 2, 2000 2:31 pm
Hello all, A while ago I misunderstood something that John Conway told me. I thought he said that almost all equilateral triangles were parallel to the Morley ...
838
xpolakis@...
May 2, 2000 3:26 pm
... For those who are not familiar with these triangles: Den Roussel's original posting to geometry-research: (see the entire discussion at: ...
839
Floor van Lamoen
f.v.lamoen@...
May 2, 2000 3:33 pm
Dear Steve, ... If you try a triangle with one obtuse angle with a quite short and a quite long leg, then the parallelism clearly is not there. ... The...
840
Richard Guy
rkg@...
May 2, 2000 3:38 pm
If you've found one homothety, you've found 18. The sides of the Morley triangles make angles (B-C)/3, (C-A)/3, (A-B)/3 with the resp sides of the original...
841
xpolakis@...
May 3, 2000 7:25 pm
Chong, Frederick - Andrews, Ronald J.: A Problem of Three Ellipses. Aust. Math. Soc. Gaz. 18, No.2, 25-27 (1991). A new proof of the following Turner's theorem...
842
Arnaud PASCAL
arnaud.pascal@...
May 3, 2000 8:14 pm
Hello everybody I have a question from one of my student who is 13yo. For a test, i ask him to draw a triangle, and ... to draw Euler line and the circonscrite...
843
Lambrou Michael
lambrou@...
May 4, 2000 9:51 am
... There are many examples. Perhaps the most famous one is the so called Euler (or Feuerbach) circle through 9 nice points. Any good Geometry book should have...
844
Arnaud PASCAL
arnaud.pascal@...
May 4, 2000 12:21 pm
Hello Michael, and all ... This boy is 13 years old, with his compass, he tried to find a circle and he draws me a circle owing by 7 points of the figure and i...
845
Floor van Lamoen
f.v.lamoen@...
May 4, 2000 3:58 pm
Dear Arnaud, There are several circles in the triangle that pass through seven or more notable points. When you mention seven points I think of the Brocard...
846
Bernard Gibert
b.gibert@...
May 5, 2000 5:07 am
Dear all, as we were into Morley's theorem recently, I tried to put some cubic inside it and I think I have found something interesting : there is a...
847
Lambrou Michael
lambrou@...
May 5, 2000 11:05 am
... I think we are puting the horse before the cart here, taking into account that the boy is young and, as it appears, it is only now his talent starts ...
848
Lambrou Michael
lambrou@...
May 5, 2000 11:14 am
... Ask the boy! ... Try on another figure, again and again. If the points, accurately drawn, keep on being on a circle, then there is a good chance that he is...
849
xpolakis@...
May 5, 2000 6:34 pm
... Dear Bernard, Is this cubic passing through centers/points of other triangle equilateral triangles (such as Stammler etc) ? Antreas PS: I append below...
850
Bernard Gibert
b.gibert@...
May 6, 2000 9:42 am
Dear Antreas, ... I don't think it does because the 3 other intersections of (K) and the circumcircle are not the vertices of an equilateral triangle. BTW,...
851
xpolakis@...
May 6, 2000 1:33 pm
Dear Bernard, ... Stammler's paper: Cutting circles and the Morley theorem. Beitr. Algebra Geom. 38, No.1, 91-93 (1997). is available online from EMIS web...
852
Dick Tahta
d.tahta@...
May 6, 2000 1:34 pm
Antreas recently wrote that ... I have remained curious about this transformation and about some inconsistencies in Lemoine's use of it. And, also, about the...
853
John Conway
conway@...
May 6, 2000 6:13 pm
... Bernard - have you investigated the group structure of this cubic? If not, I think you should, because these structures are often revealing. What you do is...
854
xpolakis@...
May 6, 2000 6:25 pm
If we draw the diagonals of a regular hexagon, we observe that they are concurrent. A natural question now is: In which other regular polygons are three (or...
855
Dick Tahta
d.tahta@...
May 7, 2000 12:49 pm
Antreas: Greetings. ... In all regular 2n-gons. (and for regular (2n+1)-gon the diagonals only intersect internally in pairs - problem posed in AMM 1951,...
856
xpolakis@...
May 7, 2000 3:28 pm
... ^^^^^^^^^^ the three major ones, I meant. ... Thanks, Dick. (See below the papers). ... For JHC's contribution to the problem see the paper #1 below. The...
857
xpolakis@...
May 8, 2000 9:32 am
... Well... I located the volume at last! On Wed 23 March '77, Hermann Heineken (U. of Wuerzburg) gave a lecture at Athens on _Regular Polygons and their...
858
Floor van Lamoen
f.v.lamoen@...
May 8, 2000 2:17 pm
Dear Hyacinthians, I know of the following minimalizers: K minimalizes the sum of squared distances to the triangle sides. G minimalizes the sum of squared...
859
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
May 8, 2000 3:13 pm
Dear hyacynthists, after some investigations, I found this : let Ea the circumellipse through the Gergonne points gB and gC and Ha the circumhyperbola through...
860
xpolakis@...
May 8, 2000 3:54 pm
... How about to ask for more, dear Floor? 1. X minimalizes the perimeter/area of its pedal/cevian triangle [I think that H minimalizes the area of its pedal =...
861
Floor van Lamoen
f.v.lamoen@...
May 8, 2000 5:28 pm
... Yes, I thought about this one. The vertices minimalize here. For pedal triangles of course the circumcircle does minimalize the area. ... Nice one! Now the...
862
John Conway
conway@...
May 8, 2000 5:42 pm
... No, I didn't solve this problem, although I did do some work on it. It was completely solved about 5 years ago by Bjorn(?) Poonen and Mike Rubinstein. ...
