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

K1230

too complicated to be written here. Click on the link to download a text file.

X(2), X(4), X(6), X(13), X(14), X(15), X(16), X(30), X(1352), X(2549), X(7735)

X(43448) → X(43456)

other points below

Geometric properties :

K1230 is the pivotal KHO-cubic obtained when the pivot P is the intersection X(43448) of the lines {X2,X99}, {X4,X6}, {X20,X187}, {X30,X1384}, {X32,X3146}, {X39,X3091}, {X76,X2996}, etc, SEARCH = 2.30425578069583. See K1191 for explanations and also CL075.

Its KHO-equation is : 2 cotω x y (y - 2 z) + √3 [x^2 (y - z) - z (2 y - z) (y + z)] = 0 where ω is the Brocard angle. Note that [ ... ] = 0 is the cubic K1207. See the analogous cubic K1223.

K1230a

Other points on K1230 :

• Q1 = {4,13} /\ {14,1352} /\ {15,2549}

• Q2 = {4,14} /\ {13,1352} /\ {16,2549}

• Q3 = {4,15} /\ {13,2549} /\ {16,1352}

• Q4 = {4,16} /\ {14,2549} /\ {15,1352}

• Q5 on {4,83}, the common tangential of X(4), X(1352), X(2549), SEARCH = 3.24641926939112

• Q6 = {4,1352} /\ {2549,7735}

• Q7 = {4,2549} /\ {1352,7735}

• Q8 = {1352,2549} /\ {4,7735}