Dear Hyacinthists, may be you will be interested by the following - I try to translate a cotation from a french maths forum -: " In the special book for the...
1542
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Oct 1, 2000 10:52 am
Dear Hyacinthists, I'm sorry but I've found some typos in my message about Morley's theorem. The end of the quotation should be : " Application : Morley's...
1543
Alexander Bogomolny
alexb@...
Oct 1, 2000 2:58 pm
Dear Jean-Pierre: The proof is beautiful, especially because it works equally well if f, g, h are defined as before +- rotations through 120 degrees. Which...
1544
Alexander Bogomolny
alexb@...
Oct 1, 2000 3:20 pm
Oops. My statement about all 27 triangles needs a correction. Of the three facts: 1. p = fix (fg) , q = fix (gh) , r = fix (hf) are the common points of the...
1545
Steve Sigur
ssigur@...
Oct 1, 2000 3:34 pm
... No, the Steiner axes were not new (or even "knew" as Antreas would say). But what was new to me, and interesting, was the connection between the triple ...
1546
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Oct 1, 2000 5:18 pm
Dear Alex and other Hyacinthists, ... 1) IHES = Institut des Hautes Etudes Scientifiques Le Bois-Marie, 35, route de Chartres, F-91440 Bures-sur-Yvette, FRANCE...
1547
xpolakis@...
Oct 1, 2000 5:27 pm
Alexander Bogomolny wrote: Dear Alex, ... The Institut des Hautes Études Scientifiques of Bures-sur-Yvette (France), is an institute of advanced research in...
1548
xpolakis@...
Oct 1, 2000 5:35 pm
REPOSTING Dear Alex, ... The Institut des Hautes Études Scientifiques of Bures-sur-Yvette (France), is an institute of advanced research in mathematics and...
1549
xpolakis@...
Oct 1, 2000 5:43 pm
... Yes, but the neologism is Conway's. It means: A property of a *K*nown object which is *NEW*. Antreas...
1550
xpolakis@...
Oct 1, 2000 6:21 pm
Dear Jean-Pierre ... ^^^^^ An ordering-French-books story: Some days ago I found in a French book catalogue the title: Memoires de Crete 1932-1965. Texte de...
1551
xpolakis@...
Oct 2, 2000 12:14 am
Let Ab, Ac be the centers of the circles passing through A and touching BC at B, C, respectively. Similarly we define Bc,Ba; Ca,Cb. I think that I have posted...
1552
Alexander Bogomolny
alexb@...
Oct 2, 2000 2:51 am
... Does anyone have an answer to that question? Did Professor Jamison answer it in his talk? My knowledge of the French education is mostly based on hearsay....
1553
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Oct 2, 2000 9:32 am
Dear Alex and other Hyacinthists, ... The official point of view in mathematical education is exactly the contrary now in France : no proof, no reasoning, no...
1554
Alexander Bogomolny
alexb@...
Oct 2, 2000 1:26 pm
Dear Jean-Pierre, thank you for your response. My apologies to other Hyacinthists for raising a question outside of the group's interests. ... Here's a quote...
1555
xpolakis@...
Oct 2, 2000 3:53 pm
I am wondering which was the first definition of Kiepert's Parabola, that is, the first geometrical property of this curve, and by whom was it discovered. Was...
1556
xpolakis@...
Oct 2, 2000 3:59 pm
... Hmmm... it seems to me that he was reading Euclid just like others who read the Bible at their last days... (with the secret hope that God will forgive...
1557
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Oct 2, 2000 4:44 pm
Dear Alex and other Hyacinthists, ... education. ... Fortunately, this reform is only one year old - for the pupils of about 16 years - and has, temporarily,...
1558
Zakir Seidov
seidov@...
Oct 2, 2000 4:49 pm
Dear Hyacinthosists, I am happy that I am a member of this egroup, and though I'm just math. amateur, I promise that I'll not bother you (too often) with too...
1559
Alexander Bogomolny
alexb@...
Oct 2, 2000 5:16 pm
... Surely reading in Greek might have endeared him on Euclid, yes. Ah, sooner or later we shall all find out whether Dieudonne got his absolution or not. But...
1560
Floor van Lamoen
f.v.lamoen@...
Oct 3, 2000 10:48 am
Jean-Pierre.EHRMANN wrote: <...> ... For Napoleon's theorem in the same way: Let f,g,h be rotations about A, B, C through pi/3. Then the fixed points are the...
1561
Floor van Lamoen
f.v.lamoen@...
Oct 3, 2000 11:09 am
... Hmmm. f^3g^3h^3 is not the identity, fgh is not a translation, but Napoleon's triangle is equilateral. What's wrong? ... Best regards, Floor....
1562
Alexander Bogomolny
alexb@...
Oct 3, 2000 12:16 pm
... The reason is the two conditions are equivalent under the assumption that j^3 = 1, where j = H(fgh). Which is not the case here since j = -1. All the best,...
1563
Floor van Lamoen
f.v.lamoen@...
Oct 3, 2000 1:43 pm
... Yes, clearly. I had overlooked that condition (from the initial message by Jean-Pierre). Thanks. Kind regards, Floor....
1564
xpolakis@...
Oct 3, 2000 5:28 pm
Let P be a point on the plane of triangle ABC. Draw six circles passing through P, and touching: circle (1b) the BC at B (1c) " C (2c) CA C ...
1565
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Oct 3, 2000 11:33 pm
... It is easy to construct the equilateral triangles A'B'C' such as A, B, C lie respectively on the lines B'C', C'A', A'B' : if F is one of the two Fermat's...
1566
xpolakis@...
Oct 4, 2000 5:41 am
... A point of the locus is H, the orthocenter of ABC, and the perspector of A'B'C', ABC is the point: (cos^2 A * cos(B-C) ::) = (cosA(cos2B + cos2C) ::) [in...
1567
xpolakis@...
Oct 4, 2000 5:35 pm
... The locus is an interesting 5th degree curve, Jean-Pierre's students found that it is a bicircular quintic with real asymptote parallel to the Euler line. ...
1568
xpolakis@...
Oct 4, 2000 8:26 pm
This directory ftp://ftp.ese-metz.fr/pub/ThProving/Otter/RP/ contains the following files (papers on algebraic curves): gl-dagstu... 41 Kb Thu Apr 27...
1569
xpolakis@...
Oct 6, 2000 5:49 pm
Let P be a point on the plane of a triangle ABC, and A'B'C' its cevian triangle. From B', C' draw parallels to BC intersecting AB, AC at Ba, Ca, respectively. ...
1570
xpolakis@...
Oct 6, 2000 7:00 pm
... In the American Mathematical Monthly appeared the following problem: Give appropriate conditions under which a simple closed curve in the plane contains...
