Dear Clark Kimberling, is it easy to add in your ETC Search table also the second coordinate? It would be more easy for us to help you in finding future errors...
Hi everyone, here is a problem I've been thinking at for a while now. ... Let B = {B_1, B_2, ..., B_n} be a collection of unit pairwise disjoint unit circular...
For n = 3, it's a known problem, the triangle-solution beeing linked to the Lemoine point. In fact there are 2 solutions wrt the two cyclic orders of the three...
... ,A_n, where ... Just try, so take any starting point X_1 on a_1. Project X_1 orthogonally on a_2 to find X_2. And so on, finally end up with X_(n+1) on...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2005volume5/FG200505index.html The editors Forum...
ForumGeom
ForumGeom@...
Mar 10, 2005 1:04 pm
11093
hi everyone, i'm dusty, i'm 17 and i live in illinois. i joined this group because i really love math and i would like to learn more outside of school. i...
Dear friends, if in the line (q+r)u + (r+p)v + (p+q)w = 0 the tripolar of the isotomic of the complement of (p : q : r) we substitute u, v, w with (y-z)/(y+z),...
Dear Geometers, Theorem 1: Let the point K the median point of the triangle A1A2A3 and K1, K2, K3 the midpoints of the sidelines A2A3, A1A3 and A1A2 ...
Welcome to a Beyond Science. Where not looking, for another Quantum leap in technology today, but a INFINITE leap for tomorrow. 100 quantum particles can do...
Dear Deoclecio, from your proof we have that the center V of the Van Lamoen circle that is the point X(1153) in ETC lies on the line KF where K is in your...
Dear Hyacinthians, the recent messages about the Van Lamoen circle leave me with another question. In Forum Geometricorum Vol 3 57-63, it is shown that for any...
I got the following question that I couldn't solve quickly myself... Construct a triangle given side a, length of (interio) angle bisector d_a and angle B. ...
Dear friends, I have found in "American Mathemathical Monthly", december 2000, a discussion about the constructibility of a triangle given the vertex A, the...
Dear Quim, you wrote ... Choose M on AG so that AG = 2.GM ==> M is the midpoint of side BC Choose N on IG so that GN = 2.IG ==> N is the Nagel point of ABC ...
Good morning (evening), Dear Hyacinthists, Floor, This is problem 31 on a book (in french) of triangle constructions that I wrote. On my systematic listing...
The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2005volume5/FG200506index.html The editors Forum...
ForumGeom
ForumGeom@...
Mar 22, 2005 3:03 pm
11106
Dear Hyacinthists, Dear Eric, I have been looking for a "true" geometric construction of both problems A(\alpha) , m_a, r and A(\alpha), m_a, r_a, where m_a is...
Dear Floor, Luis, It seems you are referring to different problems: d_a in Floor's question; d_b in Luis's answer. According to my sources, the original...
Dear Hyacinthos, Given a triangle with sides a, b, c, what is the locus of points P INSIDE this triangle whose trilinear coordinates Pa, Pb, Pc satisfy the...
Dear Barukh, Floor's problem: Construct a triangle given side a, length of (interior) angle bisector d_a and angle B. Luis' problem Construct a triangle given...
Dear Barukh, [BZ]: Given a triangle with sides a, b, c, what is the locus of points P ... *** Let ABC be a triangle with BC = a, CA = b, and AB = c. If the...
just a riddle for the beginning of the spring Let ABC a triangle in an euclidian plane. To each point M of the plane, we define the map f by M'=f(M)= the point...
Let A1A2A3....An be a regular convex n-gon.How many diagonals are there equal to A_iA_j diagonal?(i,j<n)For example if n=20 then how many diagonals are there...
For the first problem If A'B'C' is the cevian triangle of X(75) the isotomic conjugate of incenter of ABC if x=MA, y=MB, z=MC then Ptolemy's theorem gives if...
Dear Francois Rideau, for your second problem, I think that Im(g) is the inellipse in ABC and the interior of this inellipse that has contact points the traces...
That's right; cheer for that funny application of the Ptolemy inequality. Note that in both cases, the range is compact! Can you explain why? François...
Because if M' is an arbitrary point of Im(f) or Im(g) and A1B1C1 is its cevian triangle then from A1 we can take the point A2 on BC such that A1A2 and BC have...
Dear Nikolaos Yes ; In others words, two distinct points have the same tripolar coordinates if they are inverse wrt the circumcircle. So the restriction of f...
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