Mathematical constant (sorted by continued fraction representation) Guide, Meaning , Facts, Information and Description
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;] | |
| 1/2 | = 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 | = 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 | [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, ...] |
|
| 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 | [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 | [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;] | |
| 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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