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 set	Value	Continued fraction representation
		[ Base 10 ]
'0'	$mathbb\{Z\}$	= 0	[0;]
'1/2'	$mathbb\{Q\}$	= 0.5	[0; 1, 1]
'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]
'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'		≈ 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'		≈ 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]
'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'	$mathbb\{N\}$	= 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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See also

See also

★ Mathematical constant