Mathematical constant (sorted by continued fraction representation)

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

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

Symbol

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

0

= 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) ≈ 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 ? ≈ 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

= 1 [1;]

φ
≈ 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, ...]

E_B ≈ 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]

B�_L ≈ 1.08366 [1; 11, 1, 20, 2, 1, 12, 2, 2]

√2
≈ 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

= 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, ...]

K_h ≈ 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

= 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

= 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]

Symbol \|Numeral	Number set	Value	Continued fraction representation
		[ Base 10 ]
Λ		> – 2.7 · 10^-9
0		= 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)		≈ 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	?	≈ 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		= 1	[1;]
φ		≈ 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, ...]
E_B		≈ 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]
B�_L		≈ 1.08366	[1; 11, 1, 20, 2, 1, 12, 2, 2]
√2		≈ 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		= 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, ...]
K_h		≈ 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		= 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		= 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]