Hello all in geometry, I have always found the Tarry point mysterious. It is opposite the Steiner point in the circumcircle and the intersection of the ...
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ForumGeom
ForumGeom@...
Apr 3, 2006 4:19 pm
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2006volume6/FG200613index.html The editors Forum...
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Bernard Gibert
bernardgibert
Apr 3, 2006 2:46 pm
Dear Nikolaos, Isogonal conjugation (can be generalized) is a 2nd degree transform with 3 singular points A, B, C. It transforms a curve (C) of degree n into a...
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Francois Rideau
francoisrideau
Apr 3, 2006 7:01 am
Dear Jeff Here, I explain the situation: For a conic with center, a bitangent circle is called focal circle ( cercle focal in french). Those centered on the...
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Nikolaos Dergiades
ndergiades
Apr 3, 2006 4:44 am
Hello Steve, ... many thanks. And what I wrote "(the circle tPBC)" must be corrected as "(the circle gPBC)" Best regards Nikos Dergiades...
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Jeff Brooks
jbrooks_tulsa
Apr 3, 2006 3:38 am
Dear Francois, I agree with the pedal triangles of Gi and Cevian triangles of tFi being the same, but I am lost on the inscribed triangles with pivots Gi. Can...
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Steve Sigur
steve_sigur
Apr 2, 2006 10:03 pm
Peter has used the gt and tg operations in his post so I want to say a few things about those since they are not so well known. John turned me onto them. He...
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Steve Sigur
steve_sigur
Apr 2, 2006 8:59 pm
... Hello Nakolaos, I wrote an FG article that answered some of these questions a year or so ago. The title was something like "Where are the conjugates?" Your...
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Steve Sigur
steve_sigur
Apr 2, 2006 8:57 pm
... Jeff, The ancients I refer to were 100 year old ancients. I leaned it from the article by Mineur called Anallagmatic Cubics which is translated from French...
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Steve Sigur
steve_sigur
Apr 2, 2006 8:57 pm
... I am adding things to this for my benefit. I am adding the new results as well as why we know the statements are true. G+ is taken to be in the same...
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Nikolaos Dergiades
ndergiades
Apr 2, 2006 8:07 pm
Dear friends, it is known that if ABC is a triangle and P is a point in the plane of ABC not on the sides of ABC then the isogonal conjugate of the circle PBC ...
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Jeff Brooks
jbrooks_tulsa
Apr 2, 2006 7:00 pm
Dear Steve, Of course this is the basis for your geometric theory -- and a very beautiful theory it is. I am interested in learning more about the ancients...
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Steve Sigur
steve_sigur
Apr 2, 2006 6:50 pm
... Jeff, I definitely think there is something here. It is the basis for my whole geometric theory! Steve Triangle web page: ...
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peter_mows
Apr 2, 2006 4:15 pm
Dear All foci fans ... Wonderful results Wilson .. Various lines concerning the Steiner foci ... f +/-, foci of the Steiner Inellipse F +/-, foci of the...
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Bernard Gibert
bernardgibert
Apr 2, 2006 7:01 am
Dear Wilson, ... you're right. my proof is not precise enough and Thomson is just a (misplaced) coincidence. let us consider a point R and let us seek P such...
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Wilson Stothers
wilsonmaths
Apr 2, 2006 4:15 am
Dear Steve ... found ... the ... We can identify G1, G2 as follows they lie on the Darboux Cubic (as isogonals with line through X(20)) they lie on Bernards...
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Jeff Brooks
jbrooks_tulsa
Apr 2, 2006 4:03 am
Dear Steve, You may choose not to mention this one again, but I'm hanging onto it while thinking there might be something here. Sincerely, Jeff ... so ... P-- ...
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Wilson Stothers
wilsonmaths
Apr 2, 2006 3:53 am
Dear Bernard It looks a nice proof, but I have one problem ... ... in- ... This appears to suggest that P with ctP = G, K have the property that the cevian...
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Francois Rideau
francoisrideau
Apr 1, 2006 11:59 pm
... [Non-text portions of this message have been removed]...
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Steve Sigur
steve_sigur
Apr 1, 2006 6:57 pm
If f1 is mF1 (i.e., on opposite side of non-focal axis) then F1, tf1, tF1, tG1 are colinear. This means that tG1 and tf1 can be written as linear...
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Steve Sigur
steve_sigur
Apr 1, 2006 6:54 pm
... Yes there is more to this story than we have found (and we have found so much more than I ever thought was there!). G1, G2, O, H are on the Darboux cubic,...
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Steve Sigur
steve_sigur
Apr 1, 2006 6:15 pm
Wilson, François, Jean-Pierre, Bernard, Peter, and all, In checking Wilson's statements last night I noticed that there is a point on each axis of the Steiner...
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Bernard Gibert
bernardgibert
Apr 1, 2006 3:49 pm
Dear Steve , ... cP is the complement of P Best regards Bernard [Non-text portions of this message have been removed]...
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Steve Sigur
steve_sigur
Apr 1, 2006 3:25 pm
... what is "c" here? Steve Triangle web page: http://paideiaschool.org/TeacherPages/Steve_Sigur/geometryIndex.htm Other math: ...
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Steve Sigur
steve_sigur
Apr 1, 2006 3:25 pm
A correction and some new stuff ... A correction: f1--tf2 does not go though G1 or G2, but f1--O and f2-- O seem to. If G1 and G2 are on the Darboux cubic, its...
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Wilson Stothers
wilsonmaths
Apr 1, 2006 1:24 pm
Steve, A minor correction below - perhaps even more interesting! ... [SS}> Wow -- very nice. My pictures support this conjecture. Now proved by Bernard - a...
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Francois Rideau
francoisrideau
Apr 1, 2006 12:24 pm
Sorry,I mixed up Steiner circumellipse with Steiner inellipse, oops! I read your posts too quickly! That's why I went wrong! Francois [Non-text portions of...
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jpehrmfr
Apr 1, 2006 9:11 am
Dear Bernard ... Of course, you're right - in fact I was thinking to your points UVW - Looking at your nice page about Darboux, I have an obvious explanation ...
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Bernard Gibert
bernardgibert
Apr 1, 2006 8:46 am
Dear Jean-Pierre, ... THEY DO, dear Jean-Pierre ! Best regards Bernard [Non-text portions of this message have been removed]...
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jpehrmfr
Apr 1, 2006 8:35 am
Dear Bernard and Steve ... through ... I don't think so ... Darboux ... Yes, indeed. These three points are UVW in your Darboux page. many thanks. It is quite...
