LineOrder Gallery #2

Kobon 5-Lines
(5 Triangles, Mirror Symmetry)

y = mi(x - ai), i = 0..4:

ε = 1 / 10 < 1 / 8

m0 = 0, a0 = 0
m1 = -1.3763819, a1 = tan(-1𝜋/4)
m2 = -19.9833325, a2 = ε
m3 = 19.9833325, a3 = -ε
m4 = 1.3763819, a4 = tan(1𝜋/4)


For wxMaxima:
0,
-1.3763819 * (x - tan(-1 * %pi / 4)),
-19.9833325 * (x + 1/10),
19.9833325 * (x - 1/10),
1.3763819 * (x - tan(1 * %pi / 4)),

Kobon 7-Lines
(11 Triangles, Mirror Symmetry)

y = mi(x - ai), i = 0..6:

ε = 1 / 14 < 1 / 12

m0 = 0, a0 = 0
m1 = -0.7974734, a1 = tan(-1𝜋/6)
m2 = -2.0765214, a2 = tan(-2𝜋/6)
m3 = -19.9833325, a3 = ε
m4 = 19.9833325, a4 = -ε
m5 = 2.0765214, a5 = tan(2𝜋/6)
m6 = 0.7974734, a6 = tan(1𝜋/6)


For wxMaxima:
0,
-0.7974734 * (x - tan(-1 * %pi / 6)),
-2.0765214 * (x - tan(-2 * %pi / 6)),
-19.9833325 * (x + 1/14),
19.9833325 * (x - 1/14),
2.0765214 * (x - tan(2 * %pi / 6)),
0.7974734 * (x - tan(1 * %pi / 6)),

Kobon 9-Lines
(21 Triangles, Mirror Symmetry)

y = mi(x - ai), i = 0..8:

ε = 1 / 18 < 1 / 16

m0 = 0, a0 = 0
m1 = -0.5773503, a1 = tan(-3𝜋/8)
m2 = -1.1917536, a2 = tan(-1𝜋/8)
m3 = -2.7474774, a3 = tan(-2𝜋/8)
m4 = -19.9833325, a4 = ε
m5 = 19.9833325, a5 = -ε
m6 = 2.7474774, a6 = tan(2𝜋/8)
m7 = 1.1917536, a7 = tan(1𝜋/8)
m8 = 0.5773503, a8 = tan(3𝜋/8)


For wxMaxima:
0,
-0.5773503 * (x - tan(-3 * %pi / 8)),
-1.1917536 * (x - tan(-1 * %pi / 8)),
-2.7474774 * (x - tan(-2 * %pi / 8)),
-19.9833325 * (x + 1/18),
19.9833325 * (x - 1/18),
2.7474774 * (x - tan(2 * %pi / 8)),
1.1917536 * (x - tan(1 * %pi / 8)),
0.5773503 * (x - tan(3 * %pi / 8)),

11-Lines (32 Triangles)
(based on solution by Honma)
(not suitable for Proposition 3.1)

y = mi(x - ai), i = 0..10:

ε = 1 / 22 < 1 / 20

m0 = 0, a0 = 0
m1 = -0.2615465, a1 = tan(-4𝜋/10)
m2 = -1.0298714, a2 = tan(1𝜋/10)
m3 = -2.0130975, a3 = tan(-2𝜋/10)
m4 = -4.3446427, a4 = -ε
m5 = -25.5645486, a5 = tan(-3𝜋/10)
m6 = 2.7017707, a6 = tan(-1𝜋/10)
m7 = 1.4888582, a7 = ε
m8 = 1.0746682, a8 = tan(2𝜋/10)
m9 = 0.718313, a9 = tan(3𝜋/10)
m10 = 0.1670701, a10 = tan(4𝜋/10)


For wxMaxima:
0,
-0.2615465 * (x - tan(-4 * %pi / 10)),
-1.0298714 * (x - tan(1 * %pi / 10)),
-2.0130975 * (x - tan(-2 * %pi / 10)),
-4.3446427 * (x - 1/22),
-25.5645486 * (x - tan(-3 * %pi / 10)),
2.7017707 * (x - tan(-1 * %pi / 10)),
1.4888582 * (x + 1/22),
1.0746682 * (x - tan(2 * %pi / 10)),
0.718313 * (x - tan(3 * %pi / 10)),
0.1670701 * (x - tan(4 * %pi / 10)),

Kobon 13-Lines
(47 Triangles, Mirror Symmetry)
(based on solution by Kabanovitch)

y = mi(x - ai), i = 0..12:

ε = 1 / 26 < 1 / 24

m0 = 0, a0 = 0
m1 = -0.2885669, a1 = tan(-5𝜋/12)
m2 = -0.7122015, a2 = tan(-1𝜋/12)
m3 = -0.8749263, a3 = tan(-3𝜋/12)
m4 = -3.6695876, a4 = tan(-2𝜋/12)
m5 = -6.0310043, a5 = tan(-4𝜋/12)
m6 = -15.8845208, a6 = ε
m7 = 15.8845208, a7 = -ε
m8 = 6.0310043, a8 = tan(4𝜋/12)
m9 = 3.6695876, a9 = tan(2𝜋/12)
m10 = 0.8749263, a10 = tan(3𝜋/12)
m11 = 0.7122015, a11 = tan(1𝜋/12)
m12 = 0.2885669, a12 = tan(5𝜋/12)


For wxMaxima:
0,
-0.2885669 * (x - tan(-5 * %pi / 12)),
-0.7122015 * (x - tan(-1 * %pi / 12)),
-0.8749263 * (x - tan(-3 * %pi / 12)),
-3.6695876 * (x - tan(-2 * %pi / 12)),
-6.0310043 * (x - tan(-4 * %pi / 12)),
-15.8845208 * (x + 1/26),
15.8845208 * (x - 1/26),
6.0310043 * (x - tan(4 * %pi / 12)),
3.6695876 * (x - tan(2 * %pi / 12)),
0.8749263 * (x - tan(3 * %pi / 12)),
0.7122015 * (x - tan(1 * %pi / 12)),
0.2885669 * (x - tan(5 * %pi / 12)),

Kobon 17-Lines (85 Triangles)
(based on solution by Johannes Bader)

y = mi(x - ai), i = 0..16:

ε = 1 / 34 < 1 / 32

m0 = 0, a0 = 0
m1 = -0.3166485, a1 = tan(7𝜋/16)
m2 = -0.4791101, a2 = tan(-4𝜋/16)
m3 = -0.8204082, a3 = tan(3𝜋/16)
m4 = -1.0031728, a4 = tan(-6𝜋/16)
m5 = -1.6804231, a5 = tan(1𝜋/16)
m6 = -2.3663988, a6 = tan(-2𝜋/16)
m7 = -5.3495275, a7 = tan(5𝜋/16)
m8 = 26.7274944, a8 = -ε
m9 = 5.4191716, a9 = tan(2𝜋/16)
m10 = 2.378765, a10 = tan(-5𝜋/16)
m11 = 1.5246315, a11 = ε
m12 = 1.1361431, a12 = tan(-3𝜋/16)
m13 = 0.9298155, a13 = tan(4𝜋/16)
m14 = 0.4979408, a14 = tan(-1𝜋/16)
m15 = 0.241266, a15 = tan(6𝜋/16)
m16 = 0.1047156, a16 = tan(-7𝜋/16)


For wxMaxima:
0,
-0.3166485 * (x - tan(7 * %pi / 16)),
-0.4791101 * (x - tan(-4 * %pi / 16)),
-0.8204082 * (x - tan(3 * %pi / 16)),
-1.0031728 * (x - tan(-6 * %pi / 16)),
-1.6804231 * (x - tan(1 * %pi / 16)),
-2.3663988 * (x - tan(-2 * %pi / 16)),
-5.3495275 * (x - tan(5 * %pi / 16)),
26.7274944 * (x - 1/34),
5.4191716 * (x - tan(2 * %pi / 16)),
2.378765 * (x - tan(-5 * %pi / 16)),
1.5246315 * (x + 1/34),
1.1361431 * (x - tan(-3 * %pi / 16)),
0.9298155 * (x - tan(4 * %pi / 16)),
0.4979408 * (x - tan(-1 * %pi / 16)),
0.241266 * (x - tan(6 * %pi / 16)),
0.1047156 * (x - tan(-7 * %pi / 16)),