Dear friends, First of all I wish you a very happy and fruitful 2005. To start the new year let me offer a little theorem: If A'B'C' is a circumcevian...
Dear Floor and friends, may I wish all the best to all of you for this new year. ... your point is the isogonal conjugate of the infinite point of the ...
Bernard, Do you have a similar construction for PQ. the barycentric product of P and Q. I have searched for this with no success. From the (right now warm)...
Dear Bernard, ... [BG] ... Thanks, Bernard! The locus of the perspector for P on the Jerabek hyperbola is a quartic, the isogonal conjugate of the conic SUM...
Dear Floor, ... it seems that your conic decomposes into two secant lines at X110, passing through X112 and X351. please do check this Best regards Bernard ...
Dear Bernard, ... [BG] ... This is caused by a typo. The conic should be SUM b^4c^4SA(b^2-c^2)^4x^2 - a^6b^2c^2(c^2-a^2)^2(a^2-b^2)^2yz = 0 cyclic So with - in...
Dear Steve, nice to hear from you. ... I doubt there is a similar construction because of the disymmetry introduced by P and G, but maybe I'm wrong... best...
Dear Floor ... Happy New Year to you and to each Hyacinthist. ... reflections of ... (A"BC") ... Note that if A',B',C' lie on the circumcircle, the circles...
Dear Jean-Pierre, [FvL] ... [JPE] ... If we have A' and B', we can construct A", B", and then (A"B"C), and after that the common point P of (A"B"C) and the...
Dear friends! Happy New Year and Merry Christmas! One problem from solid geometry: In what intervals the area of pentagon-section of 1x1x1 cube can change? ...
Alexei Myakishev
alex_geom@...
Jan 8, 2005 12:11 pm
10984
Dear All, while playing around in GSP with various kinds of hexagons, I noticed that if a hexagon ABCDEF is circumscribed by a conic section (i.e. A, B, C, D,...
Dear Hyacinthists ... noticed ... A, B, ... six "short" ... that is ... to ... easily ... literature or ... I don't know who discovered the fact that if two...
Hi everyone, I'm a high school student and I learned about Heronian triangles recently. I'm also doing a paper on it. I'm wondering if anybody knows how to...
Monday, January 10, 2005 5:03 AM [GMT+1=CET], ... Virginia: The tangents of the semiangles of a Heronian triangle are rationals. Any pair of them must have a...
Dear Jean-Pierre, your hunch is right. I found a reference to the theorem in Coolidge's History of Conic Sections. According to Coolidge, the theorem can be ...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2005volume5/FG200501index.html The editors, Forum...
ForumGeom
ForumGeom@...
Jan 11, 2005 1:13 pm
10991
Dear Hyacinthians, At first, I wish a Happy New Year for all of you. Now I came with this olympiad problem: "I is the incenter of triangle ABC. Let B1 and C1...
... of ... variation ... area ... areas ... seen ... This problem (the first one) bears a certain similarity to the first problem from the Chinese Mathematics...
Dear all, Start with any convex hexagon. Construct a new hexagon, whose vertices are the sides middle points of the initial triangle. If we iterate this...
In the case of a n-polygon, this is the well-known problem of iterating a (n x n) circulant matrix: M = (1/2)( I +C) where C is the matrix of a circular...
... wrote: ... "I is the incenter of triangle ABC. Let B1 and C1 be the midpoints of sides AC and AB, respectively. Let B2 be the intersection of lines IC1...
... Wilhelm Fuhrmann (1833-1904) at least one publication: 'Synthetische Beweise Planimetrische Satz', 1890 an obituary in S Saalschutz, 'Zurerinnerung an W...
dick tahta
dick@...
Jan 15, 2005 4:42 pm
11000
... The following site http://felix.unife.it/Root/d-Mathematics/d-The-mathematician/t-Mathematicians-A-Z#F gives that he was a Danish mathematician and the...
Sorry the following I said ... http://felix.unife.it/Root/d-Mathematics/d-The-mathematician/t-Mathematicians-A-Z#F ... that is a Danish mathematician is not...
Saturday, January 15, 2005 9:53 PM [GMT+1=CET], ... In "Episodes in Nineteenth and Twentieth Cantury Euclidean Geometry" (chapter six: "The Fuhrmann Circle"),...
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