Continous Fractions ~ Equal to π (pi)

Continous Fractions ~ Equal to π (pi)

Calculated, programmed and compiled by our webmaster, John.
Contact John-on-Facebook or e-mail John by adding @mazes.com to his first name.

John started with 22/7 in honor of old math books and old teachers who taught that pi was equal to 22 sevenths
(which at least was more accurate than the Bible which says π is equal to 3.0 {1 Kings 7:23}).

For directions about calculating these numbers yourself, see www.MAZES.com/pi/how-to-calculate-continuous-fraction-for-pi.pdf

As we are able, we will add more denominators to this table.
www.MAZES.com/pi/continuous-fractions-equal-to-pi.htm
© 2016: John at MAZES.com

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Successive
Denominators
Integer Fraction
(some can be simplified)
Continuous Fractions approaching the value of π
(you can double-check (at least some) these calculations by copy/pasting these formulas into your computer's calculator)
Approximate Decimal Value (with wrong digits spaced off)
7 22 
7
22/73.14 28571
354 21978 
6994
 22/(7+1/354) 3.14 24077
1 7780234 
2476528
 22/(7+1/(354+1/1)) 3.1415 89354
12 7809978 
2485993
 22/(7+1/(354+1/(1+1/12))) 3.141592 91679
2 101414302 
32281175
 22/(7+1/(354+1/(1+1/(12+1/2)))) 3.1415926 46488
1 210716682 
67073203
 22/(7+1/(354+1/(1+1/(12+1/(2+1/1))))) 3.14159265 66083
7 312232492 
99386689
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/7)))))) 3.141592653 31799
2 2395079170 
762377378
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/2))))))) 3.141592653 60573
4 5103952502 
1624638540
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/4)))))))) 3.14159265358 80405
3 22806094850 
7259405456
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/3))))))))) 3.141592653589 89475
1 73527343714 
23404480409
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/1)))))))))) 3.1415926535897 65920
6 96379086188 
30678415955
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/6))))))))))) 3.14159265358979 64683
2 651433970352 
207357872959
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/2)))))))))))) 3.141592653589793 03764
2 1399632634532 
445516904597
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/2))))))))))))) 3.1415926535897932 74840
1 3450699239416 
1098391682153
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/1)))))))))))))) 3.14159265358979323 00626
1 4851732254974 
1544354341875
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/1))))))))))))))) 3.1415926535897932 42993
3 8302431494390 
2642746024028
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/3)))))))))))))))) 3.14159265358979323 76189
7 29749320472872 
9469502813765
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/7))))))))))))))))) 3.1415926535897932384 93629
1 216514451267510 
68918690340107
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/1)))))))))))))))))) 3.14159265358979323846 02230
1 246442396452626 
78445051165696
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/1))))))))))))))))))) 3.14159265358979323846 42801
3 462956847720136 
147363741505803
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/3)))))))))))))))))))) 3.141592653589793238462 38275
2 1634819995278558 
520379366628103
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/2))))))))))))))))))))) 3.1415926535897932384626 68209
1 3733060011826354 
1188269907481707
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/1)))))))))))))))))))))) 3.1415926535897932384626 32773
37 5369515999919456 
1709170026796405
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/37))))))))))))))))))))))) 3.141592653589793238462643 57313
2 202270686278431386 
64384759127604724
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/2)))))))))))))))))))))))) 3.14159265358979323846264338 10043
3 410098878876527918 
130538527459287758
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/(2+1/3))))))))))))))))))))))))) 3.141592653589793238462643383 61143
2 1432364855125105792 
455935894008534239
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/(2+1/(3+1/2)))))))))))))))))))))))))) 3.1415926535897932384626433832 43644
1 3275238895844550932 
1042540920161003237
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/(2+1/(3+1/(2+1/1))))))))))))))))))))))))))) 3.1415926535897932384626433832 89743
1 4709037138906000362 
1498933075720412238
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/(2+1/(3+1/(2+1/(1+1/1)))))))))))))))))))))))))))) 3.14159265358979323846264338327 57072
1 7984276034750551294 
2541473995881415475
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/(2+1/(3+1/(2+1/(1+1/(1+1/1))))))))))))))))))))))))))))) 3.1415926535897932384626433832 81464
7 12693313173656551656 
4040407071601827713
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/(2+1/(3+1/(2+1/(1+1/(1+1/(1+1/7)))))))))))))))))))))))))))))) 3.141592653589793238462643383279 32891
19 96789542931642366586 
30809068394352202594
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/(2+1/(3+1/(2+1/(1+1/(1+1/(1+1/(7+1/19))))))))))))))))))))))))))))))) 3.14159265358979323846264338327950 40543
3 1851542252591131316062 
589364203686762407811
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/(2+1/(3+1/(2+1/(1+1/(1+1/(1+1/(7+1/(19+1/3)))))))))))))))))))))))))))))))) 3.1415926535897932384626433832795028 68149
1 5652966280203062311700 
1799395053252243290107
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/(2+1/(3+1/(2+1/(1+1/(1+1/(1+1/(7+1/(19+1/(3+1/1))))))))))))))))))))))))))))))))) 3.14159265358979323846264338327950288 87907
6 7508215130149293737254 
2389939103521236753306
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/(2+1/(3+1/(2+1/(1+1/(1+1/(1+1/(7+1/(19+1/(3+1/(1+1/6)))))))))))))))))))))))))))))))))) 3.14159265358979323846264338327950288 36903
1 50673973212342440789994 
16130026645701179687008
 22/(7+1/(354+1/(1+1/(12+1/(2+1/(1+1/(7+1/(2+1/(4+1/(3+1/(1+1/(6+1/(2+1/(2+1/(1+1/(1+1/(3+1/(7+1/(1+1/(1+1/(3+1/(2+1/(1+1/(37+1/(2+1/(3+1/(2+1/(1+1/(1+1/(1+1/(7+1/(19+1/(3+1/(1+1/(6+1/1))))))))))))))))))))))))))))))))))) 3.141592653589793238462643383279502884 25650

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