Home page | Catalogue | Classes | Tables | Glossary | Notations | Links | Bibliography | Thanks | Downloads | Related Curves

The notations employed for cubics are the following :

K (read $\mathcal{K}$) : a general cubic (circum-scribed or not).

K+ : a cubic with three (real) concurring asymptotes.

K++ : a K+ with asymptotes concurring on the curve.

K60 : a cubic with three real asymptotes making 60° angles with one another. (see Special Isocubics §§5, 6 ,7 in Downloads page.)

K60+ : a K60 with three (real) concurring asymptotes.

K60++ : a K60+ with asymptotes concurring on the curve.

pK : a pivotal isocubic (see Special Isocubics §1.4 in Downloads page.)

pK(W, P) : pK with pole W, pivot P.

pK(M<->N, P) or pK(M x N, P) : pK with pivot P, invariant in the isoconjugation which swaps M and N.

nK : a non-pivotal isocubic (see Special Isocubics §1.5 in Downloads page.)

nK0 : a nK without term in xyz.

nK0(W, P) : nK0 with pole W, root P.

nK0(M<->N, P) or nK0(M x N, P) : nK0 with root P, invariant in the isoconjugation which swaps M and N.

nK(W, P, M) : the nK with pole W, root P passing through M.

cK : a conico-pivotal isocubic (see Special Isocubics §8 in Downloads page.)

cK(#S, P) : cK with singularity S, root P (see Special Isocubics §8 in Downloads page.)

iK : a self-inverse isocubic in the circumcircle (see Special Isocubics §4.4 in Downloads page.)

All these notations combine easily e.g. pK+, pK60, nK60++, etc.

 

A1(P), A2(P) : a generalized Allardice cubic.

K(P) : a generalized Lemoine cubic. See bibliography.

O(P) : an orthopivotal cubic. See bibliography.

T(P) : a generalized Tucker cubic. See Downloads page.

C(k), D(k) : cubics found in "Two Remarkable Pencils..." see Downloads page.

Z(P), Z(U, P), etc : cubics defined by Clark Kimberling. See TCCT p. 240 and "Cubics associated with triangles of equal areas", FG vol.1, 2001.

Z(U,P) = pK(W,U) where W is the barycentric product of I = X(1) and the isogonal conjugate of P. Z(P) = Z(P,I) = pK(X6,P).

psK : pseudo-pivotal cubics. See here.

spK : see CL055.

SpK : see CL056.

***

Other notations :

X(i) : a center in Clark Kimberling's ETC

E(i) : a center in Edward Brisse's catalogue of centers

Usual triangle centers :

I : incenter X(1), G : centroid X(2), O : circumcenter X(3)

H : orthocenter X(4), N : nine-point center X(5)

K : Lemoine point X(6), L : de Longchamps point X(20).

J. H. Conway's notations :

SA (read $S_A$) = (b^2 + c^2 - a^2)/2, SB, SC similarly

SO = SΩ = (a^2 + b^2 + c^2)/2

sa (read $s_a$) = (b + c - a)/2, sb, sc similarly

so = (a + b + c)/2