... [...] Another one: Let ABC be a triangle, and A'B'C' the pedal triangle of a point P. Let Pa, Pb, Pc be three points on the lines PA', PB', PC'...
1706
Atul Dixit
atul_dixie@...
Nov 1, 2000 4:09 pm
Respected Sirs, What is sine-triple-angle circle?How is it obtained geometrically?What are its properties? I have another two doubts:- 1)in J.Lester's article...
1707
Paul Yiu
yiu@...
Nov 1, 2000 4:21 pm
Dear Atul, At 09:39 PM 11/1/00 +0530, you wrote: ... ^^^^^^ They are! ... The alternate interior tangents are the common tangents to pairs of excircles other...
1708
Bernard Gibert
b.gibert@...
Nov 1, 2000 7:18 pm
Dear JP & Antreas, [JP] ... Of course I am, and you've done as usual a nice piece of work. I think we already had a discussion with JP in private...
1709
xpolakis@...
Nov 1, 2000 7:38 pm
I wrote (in a message I posted to the list, but mysteriously didn't receive it back. It is archived in the list's archive though ...
1710
Fred Lang
fred.lang@...
Nov 1, 2000 7:44 pm
Dear Andreas, your generalization is exactly the one of Guido M. Pinkernell in Journal of Geometry Vol 55 (1996) " Cubics Curves in the Triangle Plane". Your...
1711
xpolakis@...
Nov 1, 2000 8:14 pm
Dear Floor, I am reading the papers you very kindly sent me. I noticed a very interesting article in Bottema's _Verscheidenheden_, namely LV. Zumaar wat in een...
1712
xpolakis@...
Nov 1, 2000 8:50 pm
... Has anyone access to Thebault's article Kimberling (TCCT, pp. 234, 284) is refering to? V. Thebault: Sine-triple-angle circle. Mathesis 65(1956) 282 - 284....
1713
xpolakis@...
Nov 1, 2000 9:01 pm
Dear Fred, ... [...] ... Since I haven't that paper: Is his construction the same with mine? Thanks Antreas...
1714
Paul Yiu
yiu@...
Nov 1, 2000 9:51 pm
Dear Atul, You may be interested in a new version of my note on the Clawson point: http://www.math.fau.edu/yiu/clawsonsamplenew.ps Best regards Sincerely, Paul...
1715
xpolakis@...
Nov 2, 2000 3:00 pm
Let ABC be a triangle and AA', BB', CC' its altitudes. The incircle of the (right-angled) triangle A'BA touches BA at Bb, and the incircle of A'CA touches CA...
1716
Steve Sigur
ssigur@...
Nov 2, 2000 5:34 pm
... John is actually working on 4 books, probably soon to be 5. You can see why he needs coauthors. John and a former student, Derek Smith, are working on a...
1717
Steve Sigur
ssigur@...
Nov 2, 2000 5:34 pm
... My thanks to you, Antreas. What a wonderful group Hyacinchos has become! I want to say a bit about notation. There are many equivalent ways to express...
1718
xpolakis@...
Nov 2, 2000 6:21 pm
... .... thanks actually go to the excellent contributors we have! And a historical note: This group was created by me, but the actual idea of creation was...
1719
Fred Lang
fred.lang@...
Nov 2, 2000 6:44 pm
Dear Andreas, I think it is, I can send you a copy of this parper (and other) if you want, I only need your postal adress, bye Fred...
1720
xpolakis@...
Nov 2, 2000 9:00 pm
... Let me rewrite it: Let ABC be a triangle and AA', BB', CC' its altitudes. The incircle of A'BA touches BA at Bb A'CA CA Cc The A-excircle of...
1722
Quim Castellsaguer
qcastell@...
Nov 3, 2000 11:24 am
Dear friends, I have two questions about triangles that may seem very unusual in comparison with the problems proposed at the list. Perhaps the answers are...
1723
xpolakis@...
Nov 3, 2000 11:50 am
Let ABC be a triangle and AA', BB', CC' its altitudes. The incircle of A'BA touches BA at Bb A'CA CA Cc The A-excircle of A'BA BA B'b ...
1724
June Lester
jalester@...
Nov 3, 2000 5:04 pm
... I wrote "appears" because the result was discovered by numerical experiments, not by any synthetic or analytic proof. There may be one, or it may be...
1725
xpolakis@...
Nov 3, 2000 5:25 pm
Subject: Triangle Geometry in June Lester's Web Page. There is a section (Complex Triangle and Polygon Geometry) in JL's page at: ...
1726
Paul Yiu
yiu@...
Nov 3, 2000 5:29 pm
Dear June, Recently I was preparing a revision of a note on the Clawson point, and read this statement from your paper (which you have kindly sent me years...
1727
xpolakis@...
Nov 3, 2000 6:15 pm
Dear Paul ... This makes me think about h. coordinates which are not expressed by sidelengths. Sometimes trigonometry gives much more simple expressions. For...
1728
Floor van Lamoen
f.v.lamoen@...
Nov 3, 2000 8:53 pm
Dear Antreas, and all, ... <...> Abstract: Verscheidenheid LV. Just something in a triangle. Let U, V, W be points on the lines AH, BH and CH such that...
1729
xpolakis@...
Nov 4, 2000 2:23 pm
Let ABC be a triangle and AA', BB', CC' its altitudes. Let (1b), (1c) be the incircles of ABA', ACA', resp., and (1'b), (1'c) their reflections on AA' resp. 1...
1730
Floor van Lamoen
f.v.lamoen@...
Nov 4, 2000 3:36 pm
Dear all, I wrote: <...> ... Here N = No is Nagel's point. Sorry if that was unclear. Kind regards, Floor van Lamoen....
1731
xpolakis@...
Nov 4, 2000 11:38 pm
... Let now A"B"C" be the medial triangle of the pedal triangle A'B'C' of P. The locus of the points P such that A"B"C" be in perspective with ABC is again the...
1732
xpolakis@...
Nov 5, 2000 5:47 pm
... Let now A"B"C" be the medial triangle of the pedal triangle A'B'C' of P. The locus of the points P such that A"B"C" be in perspective with ABC is again the...
1733
Bernard Gibert
b.gibert@...
Nov 5, 2000 7:18 pm
Dear Antreas, ... The locus is a nonic decomposed into : 1). the Darboux cubic again 2). 3 circles, one through B & C and tangent at B to OB, at C to OC the...
1734
xpolakis@...
Nov 6, 2000 1:29 pm
Dear Bernard, [APH] ... Thanks! Another interesting triad of circles! [At the moment I thought that your circles were impossible: You speak of a circle...
1735
Dick Tahta
d.tahta@...
Nov 6, 2000 3:03 pm
A query - with apologies for cutting across current concerns - about ex-extra perspectors which were discussed at length by Barry and Steve some months ago: ...
