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....
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Floor van Lamoen
f.v.lamoen@xxx.xxx
Dec 23, 1999 8:23 am
Dear all, Let me start in a similar way as Clark did, and thank Antreas for coining the idea to start a discussion list and then finding a good way to really...
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Floor van Lamoen
f.v.lamoen@xxx.xxx
Dec 24, 1999 1:30 pm
Dear Steve, Steve Sigur wrote on the Fermat et al. points: <...> ... <...> ... <...> ... <...> ... <...> It is no coincidence that points on the Euler line are...
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Steve Sigur
ssigur@xxxxxxxx.xxxx
Dec 25, 1999 5:34 am
Hello all, This is my fist post to the new Hayacinthos Geometry mailing list. I thank Antreas for establishing it and hope it will prosper. The following is...
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Steve Sigur
ssigur@xxxxxxxx.xxxx
Dec 25, 1999 5:34 am
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...
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Steve Sigur
ssigur@xxxxxxxx.xxxx
Dec 25, 1999 5:34 am
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...
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Bernard Gibert
b.gibert@xxxx.xxx
Dec 25, 1999 5:18 pm
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...
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xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
(Date unavailable)
Dear Friends, Seasonal Greetings from Athens. And Happy Birthday, John! Following are some theorems / conjectures on what I call "orthial triangles". Let ABC...
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xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
(Date unavailable)
ABC right-angled triangle at A <==> sin^2(A) = sin^2(B) + sin^2(C) (Pythagorean Theorem) How about to call a triangle ABC as "pseudo-right-angled" if holds the...
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Richard Guy
rkg@xxxx.xxxxxxxx.xxx
Dec 26, 1999 4:01 pm
Many happy returns of the day, John. When will you next survive three consecutive orders of simple groups? R....
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xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
(Date unavailable)
X_76 [in Clark Kimberling's _TCCT_]: [Name]: 3rd Brocard Point. [Trilinears]: (:b^(-3):) [Geometrical Properties]: The Brocard midpoint (X_39) of the ...
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Steve Sigur
ssigur@xxxxxxxx.xxxx
Dec 27, 1999 1:03 am
on 12/26/99 6:37 PM Antreas P. Hatzipolakis wrote ... An important point. Conway calls this the Junction point, the isotomic conjugate of the symmedian point. ...
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xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
(Date unavailable)
<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...
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xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
(Date unavailable)
... Theorem #3: Theorem #3 The feet Ta, Tb, Tc, of the exsymmedians: ATa of the triangle ABaCa, BTb of the triangle BCbAb, and CTc of the triangle CBcAc, are...
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John Conway
conway@xxxx.xxxxxxxxx...
Dec 27, 1999 9:25 pm
... That's almost as bad as telling Erdos he was duplicating the cube for the last time! Looking forward to your next biquadrate, John C. PS. I never saw...
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John Conway
conway@xxxx.xxxxxxxxx...
Dec 27, 1999 10:13 pm
... Thanks! ... which should be enough for me to keep the notation in mind *** ... *** The two methods are essentially the same, since the Cevian ratios of...
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John Conway
conway@xxxx.xxxxxxxxx...
Dec 27, 1999 10:50 pm
Antreas - I shorten so that I can see all your points at once: ... So this is the line (p:q:r|0) where q or 1/q = (cosB + cosCcosA)/sinB The fire alarm's...
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xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
(Date unavailable)
... 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,...
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Barry Wolk
wolkb@xx.xxxxxxxxx.xxx
Dec 28, 1999 12:34 am
... Of course that is an equivalent property. ... [snip] ... It wasn't apparent to me either. However, the calculations are not difficult, and this converse is...
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Julio Gonzalez Cabillon
jgc@xxxxxx.xxx.xxx
Dec 28, 1999 1:27 am
... There is a well-known coaxial (*) family of circles associated with a triangle $ABC$ with centers on the Euler line of $ABC$. The family of circles that...
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Julio Gonzalez Cabillon
jgc@xxxxxx.xxx.xxx
Dec 28, 1999 2:12 am
... The term "desmic" ("desmique", in fact) was introduced by the mathematician C. Stephanos. Although one may suspect that the Greek word working here is...
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Richard Guy
rkg@xxxx.xxxxxxxx.xxx
Dec 28, 1999 4:46 pm
Stick with `coaxal' -- `coaxial' means the same thing, but is normally reserved for cylinders. R....
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Julio Gonzalez Cabillon
jgc@xxxxxx.xxx.xxx
Dec 28, 1999 5:40 pm
... ^ "coaxial cable" De gustibus non est disputandum! I, for one, prefer "coaxial". JGC -...
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xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
(Date unavailable)
... 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...
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xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
(Date unavailable)
Lucien Droussent: On the Orthocentroidal Circle. The American Math. Monthly 57 (1950) 169-171. There is also an O. Quadrangle: G. Casaux: Sur le quadrangle...
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Richard Guy
rkg@xxxx.xxxxxxxx.xxx
Dec 28, 1999 11:49 pm
See also Martin Gardner's article on the Asymmetric Propellor, somewhere in this year's Coll. Math. J. R....
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xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
(Date unavailable)
... The Asymmetric Propeller Martin Gardner A theorem, seventy years old at least and of unknown origin, says that if three congruent equilateral triangles are...
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Julio Gonzalez Cabillon
jgc@xxxxxx.xxx.xxx
Dec 28, 1999 11:02 pm
- ... See: Gardner, Martin: "The Asymmetric Propeller", _College Math Journal_, vol 30 (1999), no 1, pp 18-22. Regards, JGC -...
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xpolakis@xxxxxx.xxxxx...
xpolakis@xxxxxx.xxxxx...
(Date unavailable)
... First Paragraph: The late Leon Bankoff (he died in 1997) was a Beverly Hills, California, dentist who also was a world expert on plane geometry....In 1979...
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Julio Gonzalez Cabillon
jgc@xxxxxx.xxx.xxx
Dec 28, 1999 11:37 pm
... Which according to ZfM, the paper seems to provide two proofs of the theorem: If OAB, OCD and OEF are equilateral triangles of the same orientation then...
