這是以連分數表示排列的數學常數列表。
(無理數的常數有無限長的連分數:其最後面項為...。)
符號
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數集
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值
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連分數表示
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Λ
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> – 2.7 · 10−9
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0
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= 0
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[0;]
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M1
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≈ 0.26149 72128 47642 78375 54268 38608 69585
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[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]
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½
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= 0.5
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[0; 1, 1]
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Ω 或 W(1)
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≈ 0.56714 32904 09783 87299 99686 62210 35555
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[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, ...]
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γ
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≈ 0.57721 56649 01532 86060 65120 90082 40243
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[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, ...]
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≈ 0.61803 39887
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[0; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …]
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C2
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≈ 0.66016 18158 46869 57392 78121 10014 55577
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[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]
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β*
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≈ 0.70258
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[0; 1, 2, 2, 1, 3, 5, 1, 2, 6, 1, 1, 5]
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K
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?
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≈ 0.76422 36535 89220 66
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[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]
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B4
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≈ 0.87058 83800
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[0; 1, 6, 1, 2, 1, 2, 956, 8, 1, 1, 1, 23]
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K
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≈ 0.91596 55941 77219 01505 46035 14932 38411
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[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]
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1
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= 1
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[1;]
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B´L
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≈ 1.08366 (歷史上的猜測值,實際值為1)
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[1; 11, 1, 20, 2, 1, 12, 2, 2]
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K
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≈ 1.13198 824
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[1; 7, 1, 1, 2, 1, 3, 2, 1, 2, 1, 17, 1, 1, 2, 1, 2, 4, 1, 2]
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ρ
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≈ 1.32471 95724 47460 25960 90885 44780 97340
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[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 ...]
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√2
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≈ 1.41421 35623 73095 04880 16887 24209 69807
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[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, ...]
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μ
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≈ 1.45136 92348 83381 05028 39684 85892 027
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[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]
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EB
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≈ 1.60669 51524 15291 763
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[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, ...]
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φ
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≈ 1.61803 39887 49894 84820 45868 34365 63811
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[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, ...]
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B2
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≈ 1.90216 05823
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[1; 1, 9, 4, 1, 1, 8, 3, 4, 7, 1, 3, 3, 1, 2, 1, 1, 12, 4, 2, 1, 2, 2]
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2
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= 2
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[2;]
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α
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≈ 2.50290 78750 95892 82228 39028 73218 21578
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[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]
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e
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≈ 2.71828 18284 59045 23536 02874 71352 66249
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[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, ...]
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K0
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≈ 2.68545 20011 19507 41674
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[2; 1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2,
24, 1, 3, 2, 3, 1, 1, 1, 90]
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3
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= 3
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[3;]
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π
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≈ 3.14159 26535 89793 23846 26433 83279 50288
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[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, ...]
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4
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= 4
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[4;]
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δ
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≈ 4.66920 16091 02990 67185 32038 20466 20161
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[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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另見
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