Home page | Catalogue | Classes | Tables | Glossary | Notations | Links | Bibliography | Thanks | Downloads | Related Curves
K1066

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

X(4), X(8), X(10), X(76), X(85), X(341), X(6554), X(11607), X(14266)

vertices of the cevian triangle of X(668)

Geometric properties :

K1066 is the transform of the line X(1)X(3) under the mapping 𝚹 : P -> aQ described in page K1065 where further informations and a generalization are given.

K1066 is a nodal cubic with node X(8).

The following table gives some other centers on K1066 with reasonable 1st coordinate.

P

aQ

SEARCH

X35

b c (2 a + b + c) (a^2 + a b + b^2 - c^2) (-a^2 + b^2 - a c - c^2)

0.08364936356168702

X36

b c (-2 a + b + c) (a^2 - a b + b^2 - c^2) (-a^2 + b^2 + a c - c^2)

4.91419955774668

X57

(a - b - c)^2 (a b - b^2 + a c + 2 b c - c^2)

5.493555510910763

X65

(a + b) (a - b - c)^2 (a + c) (a^2 b - b^3 + a^2 c + 2 a b c + b^2 c + b c^2 - c^3)

5.119536724853017

X165

(a^2 - 2 a b + b^2 + 2 a c + 2 b c - 3 c^2) (a^2 + 2 a b - 3 b^2 - 2 a c + 2 b c + c^2) (a^2 b - 2 a b^2 + b^3 + a^2 c + 4 a b c - b^2 c - 2 a c^2 - b c^2 + c^3)

-6.940097500440749

X171

(b^2 + a c) (a b + c^2) (a b^2 + b^2 c + a c^2 + b c^2)

3.62107662161499

X354

(a^2 - 2 a b + b^2 - a c - b c) (a^2 - a b - 2 a c - b c + c^2) (a^2 b - 2 a b^2 + b^3 + a^2 c - 2 a b c - b^2 c - 2 a c^2 - b c^2 + c^3)

3.747174937660263

X940

(a b + b^2 + 2 a c + b c) (2 a b + a c + b c + c^2) (a b^2 + a b c + b^2 c + a c^2 + b c^2)

3.325429722838123

X982

(a^2 - a b + b^2) (a^2 - a c + c^2) (a^2 b - a b^2 + b^3 + a^2 c - a c^2 + c^3)

2.0438540641952

X986

(a^3 + b^3 + a^2 c + a b c + b^2 c) (a^3 + a^2 b + a b c + b c^2 + c^3) (a^3 b + b^4 + a^3 c + 2 a^2 b c + a b^2 c + b^3 c + a b c^2 + b c^3 + c^4)

2.409414768500768

X999

b c (-a + 2 b + 2 c) (a^2 - 4 a b + b^2 - c^2) (-a^2 + b^2 + 4 a c - c^2)

4.188949803671775

X1155

(a^2 - 2 a b + b^2 + a c + b c - 2 c^2) (a^2 + a b - 2 b^2 - 2 a c + b c + c^2) (a^2 b - 2 a b^2 + b^3 + a^2 c + 2 a b c - b^2 c - 2 a c^2 - b c^2 + c^3)

4.47799468953558

X1214

(a + b) (a - b - c)^2 (a + c) (a^2 + b^2 - c^2) (a^2 - b^2 + c^2) (a^4 b - b^5 + a^4 c + 2 a^3 b c + b^4 c + b c^4 - c^5)

2.129106163390231

X1319

(a + b - 2 c) (a - b - c)^2 (a - 2 b + c) (a^2 b - b^3 + a^2 c - 2 a b c + b^2 c + b c^2 - c^3)

1.860328383531948

X1388

(2 a + 2 b - 3 c) (a - b - c)^2 (2 a - 3 b + 2 c) (a^2 b - b^3 + a^2 c - a b c + b^2 c + b c^2 - c^3)

4.857806543351992

X1402

b^2 c^2 (a + b) (a + c) (-a + b + c)^2 (a b + b^2 + a c + c^2)

6.563286796759478

X1403

b c (-a + b + c)^2 (a b - a c + b c) (-a b + a c + b c) (b^2 - b c + c^2)

7.581282522620509

X1420

(a + b - 3 c) (a - b - c)^3 (a - 3 b + c) (a b + b^2 + a c - 2 b c + c^2)

9.642036857318288

X1429

(a - b - c)^2 (-b^2 + a c) (a b - c^2) (a^2 b^2 - a b^3 - b^3 c + a^2 c^2 + 2 b^2 c^2 - a c^3 - b c^3)

-0.982518689871115

X1460

b c (-a + b + c)^2 (a^2 + a b + a c + 2 b c) (a^2 + 2 a b + b^2 + c^2) (a^2 + b^2 + 2 a c + c^2)

5.966254359499682

X1617

(a - b - c)^3 (a^2 - 2 a b + b^2 - 2 b c + c^2) (a^2 + b^2 - 2 a c - 2 b c + c^2)

8.728924860794772

X2078

b c (-a + b + c)^2 (a^2 + a b + b^2 - 2 a c - 2 b c + c^2) (a^2 - 2 a b + b^2 + a c - 2 b c + c^2) (-2 a^2 + a b + b^2 + a c - 2 b c + c^2)

3.44305843323966

X2099

(a - b - c)^2 (2 a + 2 b - c) (2 a - b + 2 c) (a^2 b - b^3 + a^2 c + a b c + b^2 c + b c^2 - c^3)

4.689655112528867

X2283

b c (b - c)^3 (-a + b + c)^2

-20.09052399811788

X2352

b^2 c^2 (b + c) (-a^2 + b^2 + c^2) (a^3 + b^3 - a b c - a c^2 - b c^2) (-a^3 + a b^2 + a b c + b^2 c - c^3)

2.744881852775332