圆周率
圆的周长与其直径的比值; 圆盘面积与半径平方的比值; 椭圆面积与半长轴和半短轴长度乘积的比值; 的最小正实数根 幂级数 ∑ ∞ n个 = 0 ( − 1) n个 (2 n个 + 1)! x个 2 n个 + 1 (所有整数倍 π 作为解决方案)。
π
的十进制展开式 π
-
π = 3.1415926535897932384626433832795028841971693993751058209749445923078164...
-
{3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4, 1, 9, 7, 1, 6, 9, 3, 9, 9, 3, 7, 5, 1, 0, 5, 8, 2, 0, 9, 7, 4, 9, 4, 4, 5, 9, 2, 3, ...}
以360为中心的三位有效小数
1 3 2 1 3 4 4 1 5 5 (...) 355 2 356 5 357 9 358 0<--最重要的是,没有非零的十进制数字敢在它之前或之后! 359 3 \ 360 6><--令人惊讶的是,以360为中心的三个十进制[有效]数字是360,360度=2*pi弧度! 361 0 / 362 0<--最重要的是,没有非零的十进制数字敢在它前面或后面! 363 1 364 1 365 3 (...)
数字9
底座 b条 扩展 π
的二进制展开 π
-
π = 11.001001000011111101101010100010001000010110100011000010001101001100010011000110011000101000101110000000110111000001110011010001001010010000001... 2
-
{1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, ...}
底座 √ 2 扩展 π
-
π = 1000.00010001000000000000010010000000000100001000010000000010000001... √ 2
-
{1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...}
底座 ϕ 扩展 π
-
π = 100.0100101010010001010101000001010... ϕ ,
-
{1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, ...}
持续分数膨胀 π
|
-
{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, 6, 6, 99, 1, 2, 2, 6, 3, 5, 1, 1, 6, 8, 1, 7, 1, 2, 3, 7, 1, 2, 1, 1, 12, 1, 1, 1, 3, 1, 1, 8, 1, 1, 2, 1, 6, 1, 1, 5, ...}
1 / π
的十进制展开式 1 / π
-
1 π = 0.3183098861837906715377675267450287240689192914809128974953...
-
{3, 1, 8, 3, 0, 9, 8, 8, 6, 1, 8, 3, 7, 9, 0, 6, 7, 1, 5, 3, 7, 7, 6, 7, 5, 2, 6, 7, 4, 5, 0, 2, 8, 7, 2, 4, 0, 6, 8, 9, 1, 9, 2, 9, 1, 4, 8, 0, 9, 1, 2, 8, 9, 7, 4, 9, 5, 3, 3, ...}
2 π
的十进制展开式 2 π
-
τ : = 2 π = 6.283185307179586476925286766559005768394338798750211641949889184615632...
-
{6, 2, 8, 3, 1, 8, 5, 3, 0, 7, 1, 7, 9, 5, 8, 6, 4, 7, 6, 9, 2, 5, 2, 8, 6, 7, 6, 6, 5, 5, 9, 0, 0, 5, 7, 6, 8, 3, 9, 4, 3, 3, 8, 7, 9, 8, 7, 5, 0, 2, 1, 1, 6, 4, 1, 9, 4, 9, 8, 8, 9, 1, 8, 4, 6, 1, 5, 6, 3, 2, 8, 1, 2, 5, 7, 2, 4, 1, 7, ...}
持续分数膨胀 2 π
|
-
{6, 3, 1, 1, 7, 2, 146, 3, 6, 1, 1, 2, 7, 5, 5, 1, 4, 1, 2, 42, 5, 31, 1, 1, 1, 6, 2, 2, 4, 3, 12, 49, 1, 5, 1, 12, 1, 1, 1, 2, 3, 1, 2, 1, 1, 3, 1, 16, 2, 1, 1, 15, 2, 3, 6, 3, 8, ...}
π / 2
的十进制展开式 π / 2
-
π 2 = 1.570796326794896619231321691639751442098584699687552910487472296153908...
-
{1, 5, 7, 0, 7, 9, 6, 3, 2, 6, 7, 9, 4, 8, 9, 6, 6, 1, 9, 2, 3, 1, 3, 2, 1, 6, 9, 1, 6, 3, 9, 7, 5, 1, 4, 4, 2, 0, 9, 8, 5, 8, 4, 6, 9, 9, 6, 8, 7, 5, 5, 2, 9, 1, 0, 4, 8, 7, 4, ...}
2 / π
的十进制展开式 2 / π
-
2 π = 0.6366197723675813430755350534900574481378385829618257949906...
-
{6, 3, 6, 6, 1, 9, 7, 7, 2, 3, 6, 7, 5, 8, 1, 3, 4, 3, 0, 7, 5, 5, 3, 5, 0, 5, 3, 4, 9, 0, 0, 5, 7, 4, 4, 8, 1, 3, 7, 8, 3, 8, 5, 8, 2, 9, 6, 1, 8, 2, 5, 7, 9, 4, 9, 9, 0, 6, 6, ...}
4 π
的十进制展开式 4 π
-
4 π = 12.566370614359172953850573533118...
-
{1, 2, 5, 6, 6, 3, 7, 0, 6, 1, 4, 3, 5, 9, 1, 7, 2, 9, 5, 3, 8, 5, 0, 5, 7, 3, 5, 3, 3, 1, 1, 8, 0, 1, 1, 5, 3, 6, 7, 8, 8, 6, 7, 7, 5, 9, 7, 5, 0, 0, 4, 2, 3, 2, 8, 3, 8, 9, 9, 7, ...}
π / 4
的十进制展开式 π / 4
-
π 4 = 0.7853981633974483096156608458198757210492923498437764552437361480769541015715522496...
-
{7, 8, 5, 3, 9, 8, 1, 6, 3, 3, 9, 7, 4, 4, 8, 3, 0, 9, 6, 1, 5, 6, 6, 0, 8, 4, 5, 8, 1, 9, 8, 7, 5, 7, 2, 1, 0, 4, 9, 2, 9, 2, 3, 4, 9, 8, 4, 3, 7, 7, 6, 4, 5, 5, 2, 4, 3, 7, 3, ...}
4 / π
的十进制展开式 4 / π
-
4 π = 1.2732395447351626861510701069801...
-
{1, 2, 7, 3, 2, 3, 9, 5, 4, 4, 7, 3, 5, 1, 6, 2, 6, 8, 6, 1, 5, 1, 0, 7, 0, 1, 0, 6, 9, 8, 0, 1, 1, 4, 8, 9, 6, 2, 7, 5, 6, 7, 7, 1, 6, 5, 9, 2, 3, 6, 5, 1, 5, 8, 9, 9, 8, 1, 3, 3, 8, 7, 5, 2, 4, ...}
广义连分式展开 4 / π
|
-
{1, 1, 3, 4, 5, 9, 7, 16, 9, 25, 11, 36, 13, 49, 15, 64, 17, 81, 19, 100, 21, 121, 23, 144, 25, 169, 27, 196, 29, 225, 31, 256, 33, 289, 35, 324, 37, 361, 39, 400, 41, 441, 43, ...}
广义连分数 n个 -正方格诺数及其对应 n个 -正方数
三角gnomonic数及其对应三角数的广义连分式
|
-
{1, 1, 2, 3, 3, 6, 4, 10, 5, 15, 6, 21, 7, 28, 8, 36, 9, 45, 10, 55, 11, 66, 12, 78, 13, 91, 14, 105, 15, 120, 16, 136, 17, 153, 18, 171, 19, 190, 20, 210, 21, 231, 22, 253, 23, 276, 24, 300, 25, 325, 26, 351, 27, ...}
五边形gnomonic数及其对应五边形数的广义连分数
|
-
{1, 1, 4, 5, 7, 12, 10, 22, 13, 35, 16, 51, 19, 70, 22, 92, 25, 117, 28, ...}
π 2
的十进制展开式 π 2
-
π 2 = 9.869604401089358618834490999876151135313699407240790626413349376220044...
-
{9, 8, 6, 9, 6, 0, 4, 4, 0, 1, 0, 8, 9, 3, 5, 8, 6, 1, 8, 8, 3, 4, 4, 9, 0, 9, 9, 9, 8, 7, 6, 1, 5, 1, 1, 3, 5, 3, 1, 3, 6, 9, 9, 4, 0, 7, 2, 4, 0, 7, 9, 0, 6, 2, 6, 4, 1, 3, 3, ...}
π 三
的十进制展开式 π 三
-
π 三 = 31.00627668029982017547631506710139520222528856588510769414453810380639...
-
{3, 1, 0, 0, 6, 2, 7, 6, 6, 8, 0, 2, 9, 9, 8, 2, 0, 1, 7, 5, 4, 7, 6, 3, 1, 5, 0, 6, 7, 1, 0, 1, 3, 9, 5, 2, 0, 2, 2, 2, 5, 2, 8, 8, 5, 6, 5, 8, 8, 5, 1, 0, 7, 6, 9, 4, 1, 4, 4, 5, 3, 8, 1, 0, 3, ...}
近似值
近似值 π
-
√ 9.87654321 = 3.14269680529319... (1.00035146240304... × π)
-
√ 9.87 = 3.141655614481... (1.00002004107411... × π)
-
6 5 ϕ 2 = 3.14164078649987... (1.000015321181... × π)
的近似值 2π
-
21 ⋅ 299199 999999 = 6 283185 (0.99999999618119... × 2 π)
-
299199 999999 = 0 299199
-
113 π = 354.9999698556466359462787023105838259142801421293869577701...
-
e(电子) π − π = 19.99909997918947576726644298466904449606893684322510617247...
几乎是整数 π 三
-
π 三 = 31.00627668029982017547631506710139520222528856588510769414453810380639...
-
2 π 10 三 = 0.0062831853071...
另请参见
π 以其他整数为基数
-
A004601号 Pi的二进制展开。 -
A004602号 基数3中Pi的展开。 -
A004603号 基数4中Pi的展开。 -
A004604号 以5为基数的Pi展开。 -
A004605型 基数6中Pi的展开。 -
A004606号 基数7中Pi的展开。 -
A006941号 以8为基数的Pi展开。 -
A004608型 以9为基数的Pi展开。 -
A000796号 Pi的十进制展开式。 -
A068436号 以11为基数的Pi展开。 -
A068437号 以12为基数的Pi展开。 -
A068438美元 以13为基数的Pi展开。 -
A068439号 以14为基数的Pi展开。 -
A068440号 以15为基数的Pi展开。 -
A062964号 Pi输入 十六进制 .