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# Mathematical constant/Alternative sorting

Here is a sorting of mathematical constants by their representations as continued fractions:

Symbol
|Numeral
Number set Value Continued fraction representation
[ Base 10 ]
Λ   > – 2.7 · 10-9

0

$\mathbb{N}$ = 0 [0;]
C2   ≈ 0.66016 18158 46869 57392 78121 10014 55577 [0; 1, 1, 1, 16, 2, 2, 2, 2, 1, 18, 2, 2, 11, 1, 1, 2, 4, 1, 16, 3, 2, 4, 21, 2, 405, 2, 1, 33, 1, 1]
γ   ≈ 0.57721 56649 01532 86060 65120 90082 40243 [0; 1, 1, 2, 1, 2, 1, 4, 3, 13, 5, 1, 1, 8, 1, 2, 4, 1, 1, 40, 1, 11, 3, 7, 1, 7, 1, 1, 5, 1, 49]
β*   ≈ 0.70258 [0; 1, 2, 2, 1, 3, 5, 1, 2, 6, 1, 1, 5]
K $\mathbb{R}\backslash\mathbb{Q}$? ≈ 0.76422 36535 89220 66 [0; 1, 3, 4, 6, 1, 15, 1, 2, 2, 3, 1, 23, 3, 1, 1, 3, 1, 1, 7, 2, 3, 3, 18, 2, 1, 2, 1, 2, 1, 6]
B4   ≈ 0.87058 83800 [0; 1, 6, 1, 2, 1, 2, 956, 8, 1, 1, 1, 23]
K   ≈ 0.91596 55941 77219 01505 46035 14932 38411 [0; 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, 1, 11, 1, 10, 1, 9, 3, 1, 1, 1, 1, 1, 1, 2, 2]
M1   ≈ 0.26149 72128 47642 78375 54268 38608 69585 [0; 3, 1, 4, 1, 2, 5, 2, 1, 1, 1, 1, 13, 4, 2, 4, 2, 1, 33, 296, 2, 1, 5, 19, 1, 5, 1, 1, 1, 1, 1]

1

$\mathbb{N}$ = 1 [1;]
φ $\overline{\mathbb{Q}}$ ≈ 1.61803 39887 49894 84820 45868 34365 63811 [1; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
EB   ≈ 1.60669 51524 15291 763 [1, 1, 1, 1, 1, 5, 2, 1, 2, 29, 4, 1, 2, 2, 2, 2, 6, 1, 7, 1, 6, 2, 1, 1, 1, 20, 1, 3, 1, 1, 1]
B2   ≈ 1.90216 05823 [1; 1, 9, 4, 1, 1, 8, 3, 4, 7, 1, 3, 3, 1, 2, 1, 1, 12, 4, 2, 1, 2, 2]
K   ≈ 1.13198 824 [1; 7, 1, 1, 2, 1, 3, 2, 1, 2, 1, 17, 1, 1, 2, 1, 2, 4, 1, 2]
L   ≈ 1.08366 [1; 11, 1, 20, 2, 1, 12, 2, 2]
√2 $\mathbb{R}\backslash\mathbb{Q}$ ≈ 1.41421 35623 73095 04880 16887 24209 69807 [1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
μ   ≈ 1.45136 92348 83381 05028 39684 85892 027 [1, 2, 4, 1, 1, 1, 3, 1, 1, 1, 2, 47, 2, 4, 1, 12, 1, 1, 2, 2, 1, 7, 2, 1, 1, 1, 2, 30, 6, 3, 6]

2

$\mathbb{N}$ = 2 [2;]
α   ≈ 2.50290 78750 95892 82228 39028 73218 21578 [2; 1, 1, 85, 2, 8, 1, 10, 16, 3, 8, 9, 2, 1, 40, 1, 2, 3, 2, 2, 1, 17, 1, 1, 5, 3, 2, 6, 3, 5, 1,]
e   ≈ 2.71828 18284 59045 23536 02874 71352 66249 [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, 1, 1, 16, 1, 1, 18, 1, 1, 20, 1]
Kh   ≈ 2.68545 20011 19507 41674  [2; 1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2, 24, 1, 3, 2, 3, 1, 1, 1, 90]

3

$\mathbb{N}$ = 3 [3;]
π   ≈ 3.14159 26535 89793 23846 26433 83279 50288 [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, 1, 4, 2]

4

$\mathbb{N}$ = 4 [4;]
δ   ≈ 4.66920 16091 02990 67185 32038 20466 20161 [4; 1, 2, 43, 2, 163, 2, 3, 1, 1, 2, 5, 1, 2, 3, 80, 2, 5, 2, 1, 1, 1, 33, 1, 1, 53, 1, 1, 1, 1, 1]

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