... I confused with the equalities! will look at it later. Sorry! APH...
1325
xpolakis@...
Sep 2, 2000 7:57 am
... distinct ... Here is the proof (I deleted what was wrong or not needed in my previous posting): Triangle (A"B"C); Transversal C*A'B': C*B" B'C A'A" ...
1326
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Sep 2, 2000 8:24 am
... De : <xpolakis@...> À : <Hyacinthos@egroups.com> Envoyé : vendredi 1 septembre 2000 02:10 Objet : Re: [EMHL] Asymptotes of Kiepert hyperbola Dear...
1327
xpolakis@...
Sep 2, 2000 8:56 am
... I know of three remarkable concentric circles centered at I: Incircle, Adams Circle (from Gergonne point Ge draw parallels to its cevian triangle. Then...
1328
xpolakis@...
Sep 2, 2000 4:08 pm
... Some geometry monographs of Carl Adams (1811-1849), a "Lehrer der Mathematik un der Gewerbschule in Winterthur". 1. Adams, C.: Die Lehre von den...
1329
John Conway
conway@...
Sep 2, 2000 5:28 pm
... [...] ... This line contains the indirectness (which I must admit, is pretty minimal), because it really compares the "known" solution for SP,SD,CS with...
1330
John Conway
conway@...
Sep 2, 2000 6:23 pm
On Thu, 24 Aug 2000, Floor van Lamoen wrote: [about Napoleon, to which I reply that I really do consider "Napoleon" to be just a descriptive name here. In TB,...
1331
John Conway
conway@...
Sep 2, 2000 6:46 pm
... I've just tried to answer this. ... Both. Just got back from a week in Vermont, where I was out of email touch, so am frantically answering many messages....
1332
conway@...
Sep 2, 2000 7:02 pm
... No, that's quite right. The reasons it's "basic" are several. On the one hand, this Brocard image map is a similarity (actually, an anti-similarity)...
1333
Floor van Lamoen
f.v.lamoen@...
Sep 3, 2000 8:51 am
... Well, that is a relief! Thanks for your reply. Kind regards, Floor....
1334
xpolakis@...
Sep 3, 2000 8:04 pm
Let ABC be a triangle and P a point. Draw the perpendicular bisectors of PA,PB,PC, forming triangle A',B',C' [ie A' = (perp. bis. of PB) /\ (perp. bis. of PB)]...
1335
Bernard Gibert
b.gibert@...
Sep 3, 2000 9:22 pm
Dear Antreas, ... If my computation is OK, it is the reunion of : the line at infinity the circumcircle the Neuberg cubic Best regards Bernard...
1336
yiu@...
Sep 3, 2000 9:24 pm
Dear Antreas, [APH]: Let ABC be a triangle and P a point. Draw the perpendicular bisectors of PA,PB,PC, forming triangle A',B',C' [ie A' = (perp. bis. of PB)...
1337
yiu@...
Sep 3, 2000 10:03 pm
Dear Antreas and Bernard, [APH]: Let ABC be a triangle and P a point. Draw the perpendicular bisectors of PA,PB,PC, forming triangle A',B',C' [ie A' = (perp....
1338
xpolakis@...
Sep 4, 2000 1:17 am
... Ah... my memoery is too short! APH ... Date: Mon, 28 Jun 1999 14:14:39 -0400 (EDT) From: John Conway <conway@...> To: Floor van Lamoen...
1339
xpolakis@...
Sep 4, 2000 7:53 am
Feuerbach, Karl Wilhelm : Eigenschaften einiger merkwu"rdigen Punkte des geradlinigen Dreiecks und mehrerer durch sie bestimmten Linien und Figuren: Eine...
1340
xpolakis@...
Sep 4, 2000 5:16 pm
"Mo"bius's invention of homogeneous coordinates was one of the most far-reaching ideas in the history of mathematics....." (H.S.M. Coxeter: Introduction to...
1341
xpolakis@...
Sep 4, 2000 8:16 pm
A. M[onjallon] proposed in JdeME 74 (1949-50), p. 88, #14294 [solution idid. 75 (1950-51), pp. 17-18], the following problem (my English translation): Let ABC...
1342
Ken Pledger
Ken.Pledger@...
Sep 4, 2000 8:52 pm
... As often happens, the invention was not quite clear-cut even with Mo"bius. He represents each point in the plane by an expression aA + bB + cC using...
1343
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Sep 4, 2000 10:03 pm
... De : <xpolakis@...> À : <hyacinthos@egroups.com> Envoyé : lundi 4 septembre 2000 22:16 Objet : [EMHL] A.M.'s Problem Dear Antreas and other...
1344
xpolakis@...
Sep 4, 2000 10:20 pm
ABC is a triangle, and D,E,F are the midpoints of the arcs of its nine-point circle cut off by BC, CA, AB, respectively. The inscribed circle touches these...
1345
John Conway
conway@...
Sep 4, 2000 10:44 pm
... This remark was certainly worth making, but the mere fact that Mobius didn't use a notation like (a,b,c) does not make it sensible to say that he didn't...
1346
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Sep 4, 2000 11:23 pm
... De : <xpolakis@...> À : <hyacinthos@egroups.com> Envoyé : mardi 5 septembre 2000 00:20 Objet : [EMHL] Are these lines concurrent? (problem by W. J....
1347
xpolakis@...
Sep 5, 2000 5:02 pm
[APH] ... Dear Jean-Pierre, I think that it can be generalized in this way: Let ABC be a triangle and (K) a circle on its plane. From K [=circle's center] draw...
1348
xpolakis@...
Sep 5, 2000 5:16 pm
On Sun, 3 Jan 1999, John Conway (in geometry-college) mentioned the book: Benjamin Hallowell's "Geometric Analysis", published in 1872 On Tue, 5 Sep 2000, Ken...
1349
John Conway
conway@...
Sep 5, 2000 6:38 pm
... I'll see if I can find my copy. JHC...
1350
xpolakis@...
Sep 5, 2000 9:13 pm
... Dear Jean-Pierre, This result [cevian triangle ---. collinear points] reminds me another nice problem published in the same periodical: Let ABC be a...
1351
xpolakis@...
Sep 5, 2000 9:46 pm
Following is an old posting to sci.math newsgroup with a proof of Steiner-Lehmus Theorem. APH ... Subject: Re: In re angle bisector Q From: Ilias Kastanas...
1352
Jean-Pierre.EHRMANN
Jean-Pierre.EHRMANN@...
Sep 6, 2000 11:14 am
... De : <xpolakis@...> À : <Hyacinthos@egroups.com> Envoyé : mardi 5 septembre 2000 23:13 Objet : Re: [EMHL] A.M.'s Problem Dear Antreas and other...
1353
xpolakis@...
Sep 6, 2000 2:58 pm
The locus of the points whose the "distances" from two given circles are equal, are two hyperbolae (F.G.-M., paragraph 2148, of 5e edition) ["distance" of a...
