连分数逼近？

用尺子量的？

大概是计算pi的分数形式吧，也就是计算pi的小数位的问题，貌似有级数公式可以用，多算几项就可以了。

result for bestFracForMinimumError(3.14159265357989, 0.00000002)

19/6 = 3.166666666666667 has error of 0.7981306251812731 per cent
22/7 = 3.142857142857143 has error of 0.04024994378892668 per cent
44/14 = 3.142857142857143 has error of 0.04024994378892668 per cent
66/21 = 3.142857142857143 has error of 0.04024994378892668 per cent
88/28 = 3.142857142857143 has error of 0.04024994378892668 per cent
110/35 = 3.142857142857143 has error of 0.04024994378892668 per cent
132/42 = 3.142857142857143 has error of 0.04024994378892668 per cent
154/49 = 3.142857142857143 has error of 0.04024994378892668 per cent
176/56 = 3.142857142857143 has error of 0.04024994378892668 per cent
179/57 = 3.140350877192982 has error of 0.03952697004186505 per cent
201/64 = 3.140625 has error of 0.03080137009160977 per cent
223/71 = 3.140845070422535 has error of 0.02379631097663448 per cent
245/78 = 3.141025641025641 has error of 0.01804857016433563 per cent
267/85 = 3.141176470588235 has error of 0.01324751607407596 per cent
289/92 = 3.141304347826087 has error of 0.009177057171446507 per cent
311/99 = 3.141414141414141 has error of 0.005682218719717738 per cent
333/106 = 3.141509433962264 has error of 0.002648962704988730 per cent
355/113 = 3.141592920353982 has error of 0.000008491679584748133 per cent
710/226 = 3.141592920353982 has error of 0.000008491679584748133 per cent
1065/339 = 3.141592920353982 has error of 0.000008491679584748133 per cent
1420/452 = 3.141592920353982 has error of 0.000008491679584748133 per cent
1775/565 = 3.141592920353982 has error of 0.000008491679584748133 per cent
2130/678 = 3.141592920353982 has error of 0.000008491679584748133 per cent
2485/791 = 3.141592920353982 has error of 0.000008491679584748133 per cent
2840/904 = 3.141592920353982 has error of 0.000008491679584748133 per cent
3195/1017 = 3.141592920353982 has error of 0.000008491679584748133 per cent
3550/1130 = 3.141592920353982 has error of 0.000008491679584748133 per cent
3905/1243 = 3.141592920353982 has error of 0.000008491679584748133 per cent
4260/1356 = 3.141592920353982 has error of 0.000008491679584748133 per cent
4615/1469 = 3.141592920353982 has error of 0.000008491679584748133 per cent
4970/1582 = 3.141592920353982 has error of 0.000008491679584748133 per cent
5325/1695 = 3.141592920353982 has error of 0.000008491679584748133 per cent
5680/1808 = 3.141592920353982 has error of 0.000008491679584748133 per cent
6035/1921 = 3.141592920353982 has error of 0.000008491679584748133 per cent
6390/2034 = 3.141592920353982 has error of 0.000008491679584748133 per cent
6745/2147 = 3.141592920353982 has error of 0.000008491679584748133 per cent
7100/2260 = 3.141592920353982 has error of 0.000008491679584748133 per cent
7455/2373 = 3.141592920353982 has error of 0.000008491679584748133 per cent
7810/2486 = 3.141592920353982 has error of 0.000008491679584748133 per cent
8165/2599 = 3.141592920353982 has error of 0.000008491679584748133 per cent
8520/2712 = 3.141592920353982 has error of 0.000008491679584748133 per cent
8875/2825 = 3.141592920353982 has error of 0.000008491679584748133 per cent
9230/2938 = 3.141592920353982 has error of 0.000008491679584748133 per cent
9585/3051 = 3.141592920353982 has error of 0.000008491679584748133 per cent
9940/3164 = 3.141592920353982 has error of 0.000008491679584748133 per cent
10295/3277 = 3.141592920353982 has error of 0.000008491679584748133 per cent
10650/3390 = 3.141592920353982 has error of 0.000008491679584748133 per cent
11005/3503 = 3.141592920353982 has error of 0.000008491679584748133 per cent
11360/3616 = 3.141592920353982 has error of 0.000008491679584748133 per cent
11715/3729 = 3.141592920353982 has error of 0.000008491679584748133 per cent
12070/3842 = 3.141592920353982 has error of 0.000008491679584748133 per cent
12425/3955 = 3.141592920353982 has error of 0.000008491679584748133 per cent
12780/4068 = 3.141592920353982 has error of 0.000008491679584748133 per cent
13135/4181 = 3.141592920353982 has error of 0.000008491679584748133 per cent
13490/4294 = 3.141592920353982 has error of 0.000008491679584748133 per cent
13845/4407 = 3.141592920353982 has error of 0.000008491679584748133 per cent
14200/4520 = 3.141592920353982 has error of 0.000008491679584748133 per cent
14555/4633 = 3.141592920353982 has error of 0.000008491679584748133 per cent
14910/4746 = 3.141592920353982 has error of 0.000008491679584748133 per cent
15265/4859 = 3.141592920353982 has error of 0.000008491679584748133 per cent
15620/4972 = 3.141592920353982 has error of 0.000008491679584748133 per cent
15975/5085 = 3.141592920353982 has error of 0.000008491679584748133 per cent
16330/5198 = 3.141592920353982 has error of 0.000008491679584748133 per cent
16685/5311 = 3.141592920353982 has error of 0.000008491679584748133 per cent
17040/5424 = 3.141592920353982 has error of 0.000008491679584748133 per cent
17395/5537 = 3.141592920353982 has error of 0.000008491679584748133 per cent
17750/5650 = 3.141592920353982 has error of 0.000008491679584748133 per cent
18105/5763 = 3.141592920353982 has error of 0.000008491679584748133 per cent
18460/5876 = 3.141592920353982 has error of 0.000008491679584748133 per cent
18815/5989 = 3.141592920353982 has error of 0.000008491679584748133 per cent
19170/6102 = 3.141592920353982 has error of 0.000008491679584748133 per cent
19525/6215 = 3.141592920353982 has error of 0.000008491679584748133 per cent
19880/6328 = 3.141592920353982 has error of 0.000008491679584748133 per cent
20235/6441 = 3.141592920353982 has error of 0.000008491679584748133 per cent
20590/6554 = 3.141592920353982 has error of 0.000008491679584748133 per cent
20945/6667 = 3.141592920353982 has error of 0.000008491679584748133 per cent
21300/6780 = 3.141592920353982 has error of 0.000008491679584748133 per cent
21655/6893 = 3.141592920353982 has error of 0.000008491679584748133 per cent
22010/7006 = 3.141592920353982 has error of 0.000008491679584748133 per cent
22365/7119 = 3.141592920353982 has error of 0.000008491679584748133 per cent
22720/7232 = 3.141592920353982 has error of 0.000008491679584748133 per cent
23075/7345 = 3.141592920353982 has error of 0.000008491679584748133 per cent
23430/7458 = 3.141592920353982 has error of 0.000008491679584748133 per cent
23785/7571 = 3.141592920353982 has error of 0.000008491679584748133 per cent
24140/7684 = 3.141592920353982 has error of 0.000008491679584748133 per cent
24495/7797 = 3.141592920353982 has error of 0.000008491679584748133 per cent
24850/7910 = 3.141592920353982 has error of 0.000008491679584748133 per cent
25205/8023 = 3.141592920353982 has error of 0.000008491679584748133 per cent
25560/8136 = 3.141592920353982 has error of 0.000008491679584748133 per cent
25915/8249 = 3.141592920353982 has error of 0.000008491679584748133 per cent
26270/8362 = 3.141592920353982 has error of 0.000008491679584748133 per cent
26625/8475 = 3.141592920353982 has error of 0.000008491679584748133 per cent
26980/8588 = 3.141592920353982 has error of 0.000008491679584748133 per cent
27335/8701 = 3.141592920353982 has error of 0.000008491679584748133 per cent
27690/8814 = 3.141592920353982 has error of 0.000008491679584748133 per cent
28045/8927 = 3.141592920353982 has error of 0.000008491679584748133 per cent
28400/9040 = 3.141592920353982 has error of 0.000008491679584748133 per cent
28755/9153 = 3.141592920353982 has error of 0.000008491679584748133 per cent
29110/9266 = 3.141592920353982 has error of 0.000008491679584748133 per cent
29465/9379 = 3.141592920353982 has error of 0.000008491679584748133 per cent
29820/9492 = 3.141592920353982 has error of 0.000008491679584748133 per cent
30175/9605 = 3.141592920353982 has error of 0.000008491679584748133 per cent
30530/9718 = 3.141592920353982 has error of 0.000008491679584748133 per cent
30885/9831 = 3.141592920353982 has error of 0.000008491679584748133 per cent
31240/9944 = 3.141592920353982 has error of 0.000008491679584748133 per cent
31595/10057 = 3.141592920353982 has error of 0.000008491679584748133 per cent
31950/10170 = 3.141592920353982 has error of 0.000008491679584748133 per cent
32305/10283 = 3.141592920353982 has error of 0.000008491679584748133 per cent
32660/10396 = 3.141592920353982 has error of 0.000008491679584748133 per cent
33015/10509 = 3.141592920353982 has error of 0.000008491679584748133 per cent
33370/10622 = 3.141592920353982 has error of 0.000008491679584748133 per cent
33725/10735 = 3.141592920353982 has error of 0.000008491679584748133 per cent
34080/10848 = 3.141592920353982 has error of 0.000008491679584748133 per cent
34435/10961 = 3.141592920353982 has error of 0.000008491679584748133 per cent
34790/11074 = 3.141592920353982 has error of 0.000008491679584748133 per cent
35145/11187 = 3.141592920353982 has error of 0.000008491679584748133 per cent
35500/11300 = 3.141592920353982 has error of 0.000008491679584748133 per cent
35855/11413 = 3.141592920353982 has error of 0.000008491679584748133 per cent
36210/11526 = 3.141592920353982 has error of 0.000008491679584748133 per cent
36565/11639 = 3.141592920353982 has error of 0.000008491679584748133 per cent
36920/11752 = 3.141592920353982 has error of 0.000008491679584748133 per cent
37275/11865 = 3.141592920353982 has error of 0.000008491679584748133 per cent
37630/11978 = 3.141592920353982 has error of 0.000008491679584748133 per cent
37985/12091 = 3.141592920353982 has error of 0.000008491679584748133 per cent
38340/12204 = 3.141592920353982 has error of 0.000008491679584748133 per cent
38695/12317 = 3.141592920353982 has error of 0.000008491679584748133 per cent
39050/12430 = 3.141592920353982 has error of 0.000008491679584748133 per cent
39405/12543 = 3.141592920353982 has error of 0.000008491679584748133 per cent
39760/12656 = 3.141592920353982 has error of 0.000008491679584748133 per cent
40115/12769 = 3.141592920353982 has error of 0.000008491679584748133 per cent
40470/12882 = 3.141592920353982 has error of 0.000008491679584748133 per cent
40825/12995 = 3.141592920353982 has error of 0.000008491679584748133 per cent
41180/13108 = 3.141592920353982 has error of 0.000008491679584748133 per cent
41535/13221 = 3.141592920353982 has error of 0.000008491679584748133 per cent
41890/13334 = 3.141592920353982 has error of 0.000008491679584748133 per cent
42245/13447 = 3.141592920353982 has error of 0.000008491679584748133 per cent
42600/13560 = 3.141592920353982 has error of 0.000008491679584748133 per cent
42955/13673 = 3.141592920353982 has error of 0.000008491679584748133 per cent
43310/13786 = 3.141592920353982 has error of 0.000008491679584748133 per cent
43665/13899 = 3.141592920353982 has error of 0.000008491679584748133 per cent
44020/14012 = 3.141592920353982 has error of 0.000008491679584748133 per cent
44375/14125 = 3.141592920353982 has error of 0.000008491679584748133 per cent
44730/14238 = 3.141592920353982 has error of 0.000008491679584748133 per cent
45085/14351 = 3.141592920353982 has error of 0.000008491679584748133 per cent
45440/14464 = 3.141592920353982 has error of 0.000008491679584748133 per cent
45795/14577 = 3.141592920353982 has error of 0.000008491679584748133 per cent
46150/14690 = 3.141592920353982 has error of 0.000008491679584748133 per cent
46505/14803 = 3.141592920353982 has error of 0.000008491679584748133 per cent
46860/14916 = 3.141592920353982 has error of 0.000008491679584748133 per cent
47215/15029 = 3.141592920353982 has error of 0.000008491679584748133 per cent
47570/15142 = 3.141592920353982 has error of 0.000008491679584748133 per cent
47925/15255 = 3.141592920353982 has error of 0.000008491679584748133 per cent
48280/15368 = 3.141592920353982 has error of 0.000008491679584748133 per cent
48635/15481 = 3.141592920353982 has error of 0.000008491679584748133 per cent
48990/15594 = 3.141592920353982 has error of 0.000008491679584748133 per cent
49345/15707 = 3.141592920353982 has error of 0.000008491679584748133 per cent
49700/15820 = 3.141592920353982 has error of 0.000008491679584748133 per cent
50055/15933 = 3.141592920353982 has error of 0.000008491679584748133 per cent
50410/16046 = 3.141592920353982 has error of 0.000008491679584748133 per cent
50765/16159 = 3.141592920353982 has error of 0.000008491679584748133 per cent
51120/16272 = 3.141592920353982 has error of 0.000008491679584748133 per cent
51475/16385 = 3.141592920353982 has error of 0.000008491679584748133 per cent
51830/16498 = 3.141592920353982 has error of 0.000008491679584748133 per cent
52163/16604 = 3.141592387376536 has error of 0.000008473519432783496 per cent
52518/16717 = 3.141592390979243 has error of 0.000008358841707270784 per cent
52873/16830 = 3.141592394533571 has error of 0.000008245703933156445 per cent
53228/16943 = 3.141592398040489 has error of 0.000008134075266212509 per cent
53583/17056 = 3.141592401500938 has error of 0.000008023925753478684 per cent
53938/17169 = 3.141592404915837 has error of 0.000007915226142276431 per cent
54293/17282 = 3.141592408286078 has error of 0.000007807948039363902 per cent
54648/17395 = 3.141592411612532 has error of 0.000007702063719950011 per cent
55003/17508 = 3.141592414896048 has error of 0.000007597546159525419 per cent
55358/17621 = 3.141592418137450 has error of 0.000007494369129355507 per cent
55713/17734 = 3.141592421337544 has error of 0.000007392506973663446 per cent
56068/17847 = 3.141592424497114 has error of 0.000007291934736954160 per cent
56423/17960 = 3.141592427616927 has error of 0.000007192628004859380 per cent
56778/18073 = 3.141592430697726 has error of 0.000007094563126954560 per cent
57133/18186 = 3.141592433740240 has error of 0.000006997716898449000 per cent
57488/18299 = 3.141592436745177 has error of 0.000006902066783002755 per cent
57843/18412 = 3.141592439713231 has error of 0.000006807590689909726 per cent
58198/18525 = 3.141592442645074 has error of 0.000006714267228745561 per cent
58553/18638 = 3.141592445541367 has error of 0.000006622075359226783 per cent
58908/18751 = 3.141592448402752 has error of 0.000006530994645858698 per cent
59263/18864 = 3.141592451229856 has error of 0.000006441005130611444 per cent
59618/18977 = 3.141592454023291 has error of 0.000006352087332919985 per cent
59973/19090 = 3.141592456783656 has error of 0.000006264222186022139 per cent
60328/19203 = 3.141592459511535 has error of 0.000006177391100620553 per cent
60683/19316 = 3.141592462207496 has error of 0.000006091575996713692 per cent
61038/19429 = 3.141592464872098 has error of 0.000006006759080778917 per cent
61393/19542 = 3.141592467505885 has error of 0.000005922923036758421 per cent
61748/19655 = 3.141592470109387 has error of 0.000005840050994228236 per cent
62103/19768 = 3.141592472683124 has error of 0.000005758126401074279 per cent
62458/19881 = 3.141592475227604 has error of 0.000005677133087154334 per cent
62813/19994 = 3.141592477743323 has error of 0.000005597055264298044 per cent
63168/20107 = 3.141592480230765 has error of 0.000005517877526306919 per cent
63523/20220 = 3.141592482690406 has error of 0.000005439584721630376 per cent
63878/20333 = 3.141592485122707 has error of 0.000005362162176182663 per cent
64233/20446 = 3.141592487528123 has error of 0.000005285595406863958 per cent
64588/20559 = 3.141592489907097 has error of 0.000005209870312546302 per cent
64943/20672 = 3.141592492260062 has error of 0.000005134973110411624 per cent
65298/20785 = 3.141592494587443 has error of 0.000005060890272289761 per cent
65653/20898 = 3.141592496889655 has error of 0.000004987608588320437 per cent
66008/21011 = 3.141592499167103 has error of 0.000004915115166953261 per cent
66363/21124 = 3.141592501420186 has error of 0.000004843397307623774 per cent
66718/21237 = 3.141592503649291 has error of 0.000004772442691739381 per cent
67073/21350 = 3.141592505854801 has error of 0.000004702239128031441 per cent
67428/21463 = 3.141592508037087 has error of 0.000004632774807203176 per cent
67783/21576 = 3.141592510196515 has error of 0.000004564038079112753 per cent
68138/21689 = 3.141592512333441 has error of 0.000004496017611928223 per cent
68493/21802 = 3.141592514448216 has error of 0.000004428702232972580 per cent
68848/21915 = 3.141592516541182 has error of 0.000004362081056047718 per cent
69203/22028 = 3.141592518612675 has error of 0.000004296143385941461 per cent
69558/22141 = 3.141592520663023 has error of 0.000004230878782089541 per cent
69913/22254 = 3.141592522692550 has error of 0.000004166276931251647 per cent
70268/22367 = 3.141592524701569 has error of 0.000004102327870328340 per cent
70623/22480 = 3.141592526690391 has error of 0.000004039021699882161 per cent
70978/22593 = 3.141592528659319 has error of 0.000003976348775123558 per cent
71333/22706 = 3.141592530608650 has error of 0.000003914299642248911 per cent
71688/22819 = 3.141592532538674 has error of 0.000003852865070271521 per cent
72043/22932 = 3.141592534449677 has error of 0.000003792035955528643 per cent
72398/23045 = 3.141592536341940 has error of 0.000003731803353512475 per cent
72753/23158 = 3.141592538215735 has error of 0.000003672158606194114 per cent
73108/23271 = 3.141592540071333 has error of 0.000003613093087375643 per cent
73463/23384 = 3.141592541908998 has error of 0.000003554598393676067 per cent
73818/23497 = 3.141592543728987 has error of 0.000003496666344531311 per cent
74173/23610 = 3.141592545531554 has error of 0.000003439288854870266 per cent
74528/23723 = 3.141592547316950 has error of 0.000003382457935114790 per cent
74883/23836 = 3.141592549085417 has error of 0.000003326165882165635 per cent
75238/23949 = 3.141592550837196 has error of 0.000003270405024754546 per cent
75593/24062 = 3.141592552572521 has error of 0.000003215167914430185 per cent
75948/24175 = 3.141592554291624 has error of 0.000003160447166403193 per cent
76303/24288 = 3.141592555994730 has error of 0.000003106235618701131 per cent
76658/24401 = 3.141592557682062 has error of 0.000003052526173013537 per cent
77013/24514 = 3.141592559353839 has error of 0.000002999311858353903 per cent
77368/24627 = 3.141592561010273 has error of 0.000002946585926552643 per cent
77723/24740 = 3.141592562651576 has error of 0.000002894341629440168 per cent
78078/24853 = 3.141592564277954 has error of 0.000002842572409832825 per cent
78433/24966 = 3.141592565889610 has error of 0.000002791271806039923 per cent
78788/25079 = 3.141592567486742 has error of 0.000002740433515525715 per cent
79143/25192 = 3.141592569069546 has error of 0.000002690051299416433 per cent
79498/25305 = 3.141592570638214 has error of 0.000002640119046162262 per cent
79853/25418 = 3.141592572192934 has error of 0.000002590630771537342 per cent
80208/25531 = 3.141592573733892 has error of 0.000002541580554977789 per cent
80563/25644 = 3.141592575261270 has error of 0.000002492962603243674 per cent
80918/25757 = 3.141592576775246 has error of 0.000002444771250419025 per cent
81273/25870 = 3.141592578275995 has error of 0.000002397000926080832 per cent
81628/25983 = 3.141592579763692 has error of 0.000002349646059806088 per cent
81983/26096 = 3.141592581238504 has error of 0.000002302701335819693 per cent
82338/26209 = 3.141592582700599 has error of 0.000002256161406515559 per cent
82693/26322 = 3.141592584150141 has error of 0.000002210021051611553 per cent
83048/26435 = 3.141592585587290 has error of 0.000002164275178149495 per cent
83403/26548 = 3.141592587012204 has error of 0.000002118918756833185 per cent
83758/26661 = 3.141592588425040 has error of 0.000002073946790197408 per cent
84113/26774 = 3.141592589825951 has error of 0.000002029354408100907 per cent
84468/26887 = 3.141592591215085 has error of 0.000001985136899557366 per cent
84823/27000 = 3.141592592592593 has error of 0.000001941289458087503 per cent
85178/27113 = 3.141592593958618 has error of 0.000001897807531859947 per cent
85533/27226 = 3.141592595313303 has error of 0.000001854686569043323 per cent
85888/27339 = 3.141592596656791 has error of 0.000001811922017806261 per cent
86243/27452 = 3.141592597989218 has error of 0.000001769509549134308 per cent
86598/27565 = 3.141592599310720 has error of 0.000001727444834013012 per cent
86953/27678 = 3.141592600621432 has error of 0.000001685723575258909 per cent
87308/27791 = 3.141592601921485 has error of 0.000001644341603012490 per cent
87663/27904 = 3.141592603211009 has error of 0.000001603294779245236 per cent
88018/28017 = 3.141592604490131 has error of 0.000001562579061421590 per cent
88373/28130 = 3.141592605758976 has error of 0.000001522190470667977 per cent
88728/28243 = 3.141592607017668 has error of 0.000001482125059941808 per cent
89083/28356 = 3.141592608266328 has error of 0.000001442378977693459 per cent
89438/28469 = 3.141592609505076 has error of 0.000001402948404204296 per cent
89793/28582 = 3.141592610734028 has error of 0.000001363829647079640 per cent
90148/28695 = 3.141592611953302 has error of 0.000001325018950262833 per cent
90503/28808 = 3.141592613163010 has error of 0.000001286512748683151 per cent
90858/28921 = 3.141592614363265 has error of 0.000001248307445438879 per cent
91213/29034 = 3.141592615554178 has error of 0.000001210399507290281 per cent
91568/29147 = 3.141592616735856 has error of 0.000001172785528321575 per cent
91923/29260 = 3.141592617908407 has error of 0.000001135462070785990 per cent
92278/29373 = 3.141592619071937 has error of 0.000001098425760598732 per cent
92633/29486 = 3.141592620226548 has error of 0.000001061673350998962 per cent
92988/29599 = 3.141592621372344 has error of 0.000001025201531563864 per cent
93343/29712 = 3.141592622509424 has error of 9.890071510255648E-7 per cent
93698/29825 = 3.141592623637888 has error of 9.530870262852023E-7 per cent
94053/29938 = 3.141592624757833 has error of 9.174380697368807E-7 per cent
94408/30051 = 3.141592625869355 has error of 8.820572256056924E-7 per cent
94763/30164 = 3.141592626972550 has error of 8.469414381167303E-7 per cent
95118/30277 = 3.141592628067510 has error of 8.120877788190413E-7 per cent
95473/30390 = 3.141592629154327 has error of 7.774933192616726E-7 per cent
95828/30503 = 3.141592630233092 has error of 7.431551628246598E-7 per cent
96183/30616 = 3.141592631303893 has error of 7.090705083810046E-7 per cent
96538/30729 = 3.141592632366820 has error of 6.752364911417314E-7 per cent
96893/30842 = 3.141592633421957 has error of 6.416504373037960E-7 per cent
97248/30955 = 3.141592634469391 has error of 6.083095775711888E-7 per cent
97603/31068 = 3.141592635509206 has error of 5.752112381408658E-7 per cent
97958/31181 = 3.141592636541484 has error of 5.423528088717603E-7 per cent
98313/31294 = 3.141592637566307 has error of 5.097316796228055E-7 per cent
98668/31407 = 3.141592638583755 has error of 4.773453039149120E-7 per cent
99023/31520 = 3.141592639593909 has error of 4.451911034380017E-7 per cent
99378/31633 = 3.141592640596845 has error of 4.132666590369395E-7 per cent
99733/31746 = 3.141592641592642 has error of 3.815694560636247E-7 per cent
100088/31859 = 3.141592642581374 has error of 3.500971390248994E-7 per cent
100443/31972 = 3.141592643563118 has error of 3.188472569346401E-7 per cent
100798/32085 = 3.141592644537946 has error of 2.878175179616661E-7 per cent
101153/32198 = 3.141592645505932 has error of 2.570055666128198E-7 per cent
101508/32311 = 3.141592646467147 has error of 2.264091428879092E-7 per cent
101863/32424 = 3.141592647421663 has error of 1.960259549557538E-7 per cent
102218/32537 = 3.141592648369549 has error of 1.658538064781388E-7 per cent
102573/32650 = 3.141592649310873 has error of 1.358905329478384E-7 per cent
102928/32763 = 3.141592650245704 has error of 1.061339380266377E-7 per cent
103283/32876 = 3.141592651174109 has error of 7.658188903829936E-8 per cent
103638/32989 = 3.141592652096153 has error of 4.723231696856316E-8 per cent
103993/33102 = 3.141592653011903 has error of 1.808308914119166E-8 per cent
count is 310

化圆为方？？

在半径为r的圆中，作一个内接正六边形。这时，正六边形的边长等于圆的半径r，因此，正六边形的周长等于6r。如果把圆内接正六边形的周长看作圆的周长的近似值，然后把圆内接正六边形的周长与圆的直径的比看作为圆的周长与圆直径的比，这样得到的圆周率是3，显然这是不精确的。 我们就得到了一种计算圆周率π的近似值的方法。 早在一千七百多年前，我国古代数学家刘徽曾用割圆术求出圆周率是3.141024。继刘徽之后，我国古代数学家祖冲之在推求圆周率的研究方面，又有了重要发展。他计算的结果共得到两个数：一个是盈数（即过剩的近似值），为3.1415927；另一个是（nǜ）数（即不足的近似值），为3.1415926。圆周率的真值正好在盈两数之间。祖冲之还采用了两个分数值：一个是22/7（约等于3.14），称之为“约率”；另一个是355/113（约等于3.1415929），称之为“密率”。祖冲之求得的密率，比外国数学家求得这个值，至少要早一千年。 ⑴ 2∕π＝√2∕2*√（2＋√2）∕2*√（2＋√（2＋√2））∕2……
⑵ π∕2＝2*2*4*4*6*6*8*8……∕（1*3*3*3*4*5*5*7*7……）
⑶ π∕4＝4arctg(1∕5）-arctg（1∕239） （注：tgx=…………）
⑷ π＝426880√10005∕（∑(（6n）！*（545140134n+13591409)) ∕（（n！）*（3n)！*（-640320）＾（3n)))
（0≤n→∞）

看了半天原来是google大叔。

饮水思源的答案很清晰。谢谢。

是啊.很利害

实际上祖冲之的算法已经遗失了，现在没人知道他当时是怎么算的

割圆术。。。

看来是后人给算的：
圆内接正12288边形和正24576边形的边长而得出来

根据《隋书·律历志》的记载，祖冲之把一丈化为一亿忽，以此为直径求圆周率。他计算的结果共得到两个数：一个是盈数（即过剩的近似值），为3.1415927；一个是朒数（即不足的近似值），为3.1415926。圆周率真值正好在盈朒两数之间。《隋书》只有这样简单的记载，没有具体说明他是用什么方法计算出来的。不过从当时的数学水平来看，除刘徽的割圆术外，还没有更好的方法。祖冲之很可能就是采用了这种方法。因为采用刘徽的方法，把圆的内接正多边形的边数增多到24576边时，便恰好可以得出祖冲之所求得的结果。

　　盈朒 两数可以列成不等式，如：3.1415926（*）＜π（真实的圆周率）＜3.1415927（盈），这表明圆周率应在盈朒 两数之间。按照当时计算都用分数的习惯，祖冲之还采用了两个分数值的圆周率。一个是355/113（约等于3.1415927），这一个数比较精密，所以祖冲之称它为“密率”。另一个是了（约等于3.14），这一个数比较粗疏，所以祖冲之称它为“约率”。在欧洲，直到1573年才由德国数学家渥脱求出了355/113这个数值。因此，日本数学家三上义夫曾建议把355/113这个圆周率数值称为“祖率”，来纪念这位中国的大数学家。

　　由于祖冲之所著的数学专著《缀术》已经失传，《隋书》又没有具体地记载他求圆周率的方法，因此，我国研究祖国数学遗产的专家们，对于他求圆周率的方法还有不同的见解。

　　有人认为祖冲之圆周率中的“朒数”。是用作圆的内接正多边形的方法求得的；而“盈数”则是用作圆的外切正多边形的方法求得的。祖冲之如果继续用刘徽的办法，从圆的内接正六边形算起，逐次加倍边数，一直算到内接正24576边形时，它的各边长度总和只能逐次接近并较小于圆周的周长，这正多边形的面积也只能逐次接近并较小于圆面积，从此求出的圆周率为3.14159261，也只能小于圆周率的真实数值，这就是朒 数。从祖冲之的数学水平来看，突破刘徽的方法，从外切正六边形算起，逐次试求圆周率，也是可能的。如果祖冲之把外切正六边形的边数成倍增加，到正24576边形时，他所求得的圆周率应该是3.14159270208。这个数是用外切方法求得的。由于外切正多边形各边边长的总和永远大于圆周的长度，这正多边形的面积也永远大于圆面积，所以这个数总比真实的圆周率大。用四舍五入法舍去小数点七位以后的数字，就得出盈数。

　　祖冲之究竟是否同时用过内接和外切这两个方法求出圆周率的朒数和盈数，是没有确切史料可以证实的。但是采用这个办法所求出的朒、盈两个数值，和祖冲之原来所求出的结果大体是一致的。所以有些数学史家认为祖冲之曾用过作圆的外切正多边形的方法求得圆周率，是很近情理的推想。

　　但是根据另一些数学史家的研究，盈、朒两数也可以由计算圆内接正12288边形和正24576边形的边长而得出来。不过这种计算比较难懂，这里不说了。

　　尽管说法有出入，但是祖冲之曾经求得“密率”，并且明确地用上、下两限来说明圆周率这个数值的范围，是可以肯定的。在一千五百年前，他有这样的成就和认识，真值得我们钦佩。

　　在推算圆周率时，祖冲之付出了不知多少辛勤的劳动。如果从正六边形算起，算到24576边时，就要把同一运算程序反复进行十二次，而且每一运算程序又包括加减乘除和开方等十多个步骤。我们现在用纸笔算盘来进行这样的计算，也是极其吃力的。当时祖冲之进行这样繁难的计算，只能用筹码（小竹棍）来逐步推演。如果头脑不是十分冷静精细，没有坚韧不拔的毅力，是绝对不会成功的。祖冲之顽强刻苦的研究精神，是很值得推崇的。

　　祖冲之死后，他的儿子祖暅（xuan玄）继续父亲的研究，进一步发现了计算圆球体积的方法。

　　在我国古代数学著作《九章算术》中，曾列有计算圆球体积的公式，但很不精确。刘徽虽然曾经指出过它的错误，但究竟应当怎样计算，他也没有求得解决。经祖暅刻苦钻研，终于找到了正确的计算方法。他所推算出的计算圆球体积的公式是：圆球体积=π/c D（D代表球体直径）。这个公式一直到今天还被人们采用着。

　　祖冲之还曾写过《缀术》五卷，是一部内容极为精采的数学书，很受人们重视。唐朝的官办学校的算学科中规定：学员要学《缀术》四年；政府举行数学考试时，多从《缀术》中出题。后来这部书曾经传到朝鲜和日本。可惜到了北宋中期，这部有价值的著作竟失传了

阿基米德用正96边形割圆术得出圆周率介乎223/71 ~ 22/7之间。
阿基米德是科学的研究圆周率的第一人。他提出用圆内接多边形与外切多边形边数增多、面积逐渐接近的方法求圆周率。他求出了圆周率大小范围为：223/71<π<22/7。