Mathematical constants (sorted by continued fraction representation)

This is a list of mathematical constants sorted by their representations as continued fractions:

(Constants known to be irrational have infinite continued fractions: their last term is ....)

Symbol
Numeral
Number setValue Continued fraction representation
[ Base 10 ]

0

mathbb{Z} = 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]
Ω or W(1) mathbb{R} ackslash mathbb{A} ≈ 0.56714 32904 09783 87299 99686 62210 35555 [0; 1, 1, 3, 4, 2, 10, 4, 1, 1, 1, 1, 2, 7, 306, 1, 5, 1, 2, 1, 5, 1, 1, 1, 1, 7, 1, 4, 2, ...]
β* ≈ 0.70258 [0; 1, 2, 2, 1, 3, 5, 1, 2, 6, 1, 1, 5, ...]
K mathbb{R}ackslashmathbb{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]
1/2 mathbb{Q} = 0.5 [0; 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;]
ρ mathbb{A} ackslash mathbb{Q} ≈ 1.32471 95724 47460 25960 90885 44780 97340 [1; 1, 3, 12, 1, 1, 3, 2, 3, 2, 4, 2, 141, 80, 2, 5, 1, 2, 8, 2, 1, 1, 3, 1, 8, 2, 1, 1, 14, 1, 1, 2, 1, 1, 1, 3, 1, 10, 4 ...]
φ mathbb{A} ackslash 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 mathbb{R} ackslash mathbb{Q} ≈ 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{A}ackslashmathbb{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" mathbb{R} ackslash mathbb{A} ≈ 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]
P2 mathbb{R} ackslash mathbb{A} ≈ 2.29558 71493 92638 07403 42980 [2; 3, 2, 1, 1, 1, 1, 3, 3, 1, 1, 4, 2, 3, 2, 7, 1, 6, 1, 8, 7, 2, 1, 61, 1, 1, 1, 1, 2, 11, 1, 1, ...]

3

mathbb{N} = 3 [3;]
π mathbb{R} ackslash mathbb{A} ≈ 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, ...]
ψ mathbb{Q} ≈ 3.35988 56662 43177 55317 20113 02918 92717 96889 [3; 2, 1, 3, 1, 1, 13, 2, 3, 3, 2, 1, 1, 6, 3, 2, 4, 362, 2, 4, 8, 6, 30, 50, 1, 6, 3, 3, 2, 7, 2, 3, 1, 3, 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]

ee also

* Mathematical constant


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