Rappresentazione come frazione continua centrata delle radici quadrate degli interi (non quadrati) fino a 100

La tabella seguente mostra la rappresentazione come frazione continua centrata delle radici quadrate degli interi (non quadrati) fino a 100 (M. Fiorentini, 2013).

n

Valore approssimato di

Frazione continua per

2

1.4142135624

[ 1+; 2+ ]

3

1.7320508076

[ 2–; 4– ]

5

2.2360679775

[ 2+; 4+ ]

6

2.4494897428

[ 2+; 2+, 4+ ]

7

2.6457513111

[ 3–; 3–, 6– ]

8

2.8284271247

[ 3–; 6– ]

10

3.1622776602

[ 3+; 6+ ]

11

3.3166247904

[ 3+; 3+, 6+ ]

12

3.4641016151

[ 3+; 2+, 6+ ]

13

3.6055512755

[ 4–; 3–, 2+, 7– ]

14

3.7416573868

[ 4–; 4–, 8– ]

15

3.8729833462

[ 4–; 8– ]

17

4.1231056256

[ 4+; 8+ ]

18

4.2426406871

[ 4+; 4+, 8+ ]

19

4.3588989435

[ 4+; 3–, 5–, 3+, 8+ ]

20

4.4721359550

[ 4+; 2+, 8+ ]

21

4.5825756950

[ 5–; 2+, 3–, 2+, 9– ]

22

4.6904157598

[ 5–; 3+, 4+, 3–, 10– ]

23

4.7958315233

[ 5–; 5–, 10– ]

24

4.8989794856

[ 5–; 10– ]

26

5.0990195136

[ 5+; 10+ ]

27

5.1961524227

[ 5+; 5+, 10+ ]

28

5.2915026221

[ 5+; 3+, 2+, 3+, 10+ ]

29

5.3851648071

[ 5+; 3–, 2+, 2+, 10+ ]

30

5.4772255751

[ 5+; 2+, 10+ ]

31

5.5677643628

[ 6–; 2+, 3+, 5+, 4–, 2+, 11– ]

32

5.6568542495

[ 6–; 3–, 12– ]

33

5.7445626465

[ 6–; 4–, 12– ]

34

5.8309518948

[ 6–; 6–, 12– ]

35

5.9160797831

[ 6–; 12– ]

37

6.0827625303

[ 6+; 12+ ]

38

6.1644140030

[ 6+; 6+, 12+ ]

39

6.2449979984

[ 6+; 4+, 12+ ]

40

6.3245553203

[ 6+; 3+, 12+ ]

41

6.4031242374

[ 6+; 2+, 2+, 12+ ]

42

6.4807406984

[ 6+; 2+, 12+ ]

43

6.5574385243

[ 7–; 2+, 4–, 7–, 5–, 2+, 13– ]

44

6.6332495807

[ 7–; 3–, 4–, 3–, 14– ]

45

6.7082039325

[ 7–; 3+, 2+, 3–, 14– ]

46

6.7823299831

[ 7–; 5–, 2+, 2+, 6+, 3–, 2+, 4–, 14– ]

47

6.8556546004

[ 7–; 7–, 14– ]

48

6.9282032303

[ 7–; 14– ]

50

7.0710678119

[ 7+; 14+ ]

51

7.1414284285

[ 7+; 7+, 14+ ]

52

7.2111025509

[ 7+; 5–, 4–, 5+, 14+ ]

53

7.2801098893

[ 7+; 4–, 2+, 3+, 14+ ]

54

7.3484692283

[ 7+; 3–, 8–, 3+, 14+ ]

55

7.4161984871

[ 7+; 2+, 2+, 2+, 14+ ]

56

7.4833147735

[ 7+; 2+, 14+ ]

57

7.5498344353

[ 8–; 2+, 5–, 2+, 15– ]

58

7.6157731059

[ 8–; 3–, 3–, 2+, 15– ]

59

7.6811457479

[ 8–; 3+, 7+, 3–, 16– ]

60

7.7459666924

[ 8–; 4–, 16– ]

61

7.8102496759

[ 8–; 5+, 4–, 3+, 3–, 4+, 5–, 16– ]

62

7.8740078740

[ 8–; 8–, 16– ]

63

7.9372539332

[ 8–; 16– ]

65

8.0622577483

[ 8+; 16+ ]

66

8.1240384046

[ 8+; 8+, 16+ ]

67

8.1853527719

[ 8+; 5+, 3–, 2+, 8–, 2+, 2+, 5+, 16+ ]

68

8.2462112512

[ 8+; 4+, 16+ ]

69

8.3066238629

[ 8+; 3+, 4–, 6–, 4+, 3+, 16+ ]

70

8.3666002653

[ 8+; 3–, 4–, 3+, 16+ ]

71

8.4261497732

[ 8+; 2+, 3–, 9–, 3+, 2+, 16+ ]

72

8.4852813742

[ 8+; 2+, 16+ ]

73

8.5440037453

[ 9–; 2+, 5+, 6–, 2+, 17– ]

74

8.6023252670

[ 9–; 3–, 2+, 17– ]

75

8.6602540378

[ 9–; 3–, 18– ]

76

8.7177978871

[ 9–; 4–, 2+, 5+, 4+, 6–, 2+, 3–, 18– ]

77

8.7749643874

[ 9–; 4+, 2+, 4–, 18– ]

78

8.8317608663

[ 9–; 6–, 18– ]

79

8.8881944173

[ 9–; 9–, 18– ]

80

8.9442719100

[ 9–; 18– ]

82

9.0553851381

[ 9+; 18+ ]

83

9.1104335791

[ 9+; 9+, 18+ ]

84

9.1651513899

[ 9+; 6+, 18+ ]

85

9.2195444573

[ 9+; 5–, 2+, 4+, 18+ ]

86

9.2736184955

[ 9; 4–, 3–, 10–, 3–, 4+, 18+ ]

87

9.3273790531

[ 9+; 3+, 18+ ]

88

9.3808315196

[ 9+; 3–, 3–, 3+, 18+ ]

89

9.4339811321

[ 9+; 2+, 3+, 3+, 2+, 18+ ]

90

9.4868329805

[ 9+; 2+, 18+ ]

91

9.5393920142

[ 10–; 2+, 6–, 7–, 2+, 19– ]

92

9.5916630466

[ 10–; 2+, 2+, 4+, 3–, 2+, 19– ]

93

9.6436507610

[ 10–; 3–, 5+, 6+, 5–, 3–, 20– ]

94

9.6953597148

[10–; 3+, 4–, 2+, 6–, 10–, 7–, 2+, 3+, 3–, 20– ]

95

9.7467943448

[ 10–; 4–, 20– ]

96

9.7979589711

[ 10–; 5–, 20– ]

97

9.8488578018

[ 10–; 7–, 3–, 3–, 2+, 6–, 20– ]

98

9.8994949366

[ 10–; 10–, 20– ]

99

9.9498743711

[ 10–; 20– ]