As I am reading some old messages sent by Steve about Anallagmatic Cubics I have found in message 2300 the terms "supplementary" and "antisupplementary" paired...
Dear Atul and other Hyacinthists ... sides of ... Let P =(x,y,z) in barycentrics. As the length of the sides of the square inscribed in ABC is 2ad/(aa+2d)where...
Dear Jean-Pierre, [JPE] ... -- I think that we have seen this problem before, and also its parametrizations. Let ABC be a triangle and P = (x:y:z) a point in...
Let ABC be a triangle, and AbAcA'cA'b, BcBaB'cB'a, CaCbC'bC'a the three similar rectangles inscribed in ABC, based on BC, CA, AB, resp., whose Height / Base =...
Dear Antreas ... inscribed ... )] ::) ... I'm sorry but I didn't remember this discussion. Note that the locus of the pivot is the hyperbola through G, the ...
Dear Atul ... doesn't ... as "Congruent ... a ... There is nothing in the Weinsstein CRC except the definition and I don't have Clark's article. What I wanted...
Dear Jean-Pierre, [APH]: [parameters corrected] ... Probably yes, probably no! I don't remember. ... Do you mean congruent = with both equal bases and equal...
... For a plane triangle A1A2A3, call two circles within the triangle <i>companion incircles</i> if they are the incircles of two triangles formed by dividing...
Dear Antreas and other Hyacinthists ... through I ... heights. [JPE] ... May be, this needs a little explanation. I've discovered (but I guess that I'm not the...
Dear Antreas and all Hyacinthists I have the article of Tucker in the Messenger of Mathematics. The ''cosine'' orthoncentres of a triangle ABC are the points...
On Wednesday, December 5, 2001, at 11:51 PM, Antreas P. Hatzipolakis ... But what are these greek letters anyway? If are angles (B,C), then the locus is the...
... Assuming that gamma, beta are sides, I translate it into Triangle geometry language: Let ABC be a triangle and P a point. Which is the locus of P such that...
Dear Hyancinthians, Let Z(U) be the cubic ux(yy-zz)+...=0 (trilinears). (1) If X is on Z(U), then the U-Ceva conjugate of X is on Z(U). (Is this known?)...
On Thursday, December 6, 2001, at 12:23 AM, Antreas P. Hatzipolakis ... Generalization: Let ABC be a triangle and P a point. Which is the locus of P such that...
Dear all and Antreas, Sorry, I thought this was standard notation. \beta = internal angle at B \gamma = internal angle at C And I vaguely recall this problem...
Let ABC be a triangle, and BCC1B1, CAA2C2, ABB3A3 the three squares based on BC,CA,AB outwardly ABC. Ba = BC /\ AA2, Ca = BC /\ AA3, Similarly Cb, Ab; Bc, Ac. ...
Dear all Hycinthists There is an error in my pervious message 4485. The Tucker cubic is, in trilinears : line_at_infinity * Steiner circuumellipse = k abc xyz ...
4497
Steve Sigur
ssigur@...
Dec 6, 2001 9:36 pm
... Yes, this was thrashed out on Hyacinthos two summer ago, when we used the term "cevian quotient" for "ceva-conjugate." The cevian quotient and the ...
Dear Antreas, [APH]: Let ABC be a triangle, and BCC1B1, CAA2C2, ABB3A3 the three squares based on BC,CA,AB outwardly ABC. Ba = BC /\ AA2, Ca = BC /\ AA3,...
Dear all, With X a point and C a circle, let P(X,C) denote the power of X with respect to C. Find the locus of P for which Pow(A,(PBC)) + Pow(B,(APC)) +...
