Pythagorean hypotenuses as contraharmonic means

Pythagorean hypotenuses as contraharmonic means

c

2

=

a

2

+

b

2

c

=

u

2

+

v

2

u

+

v

N.B.

5

2

=

3

2

+

4

2

5

=

(

2

2

+

6

2

)

/

(

2

+

6

)

3

10

2

=

6

2

+

8

2

10

=

(

6

2

+

12

2

)

/

(

6

+

12

)

13

2

=

5

2

+

12

2

13

=

(

3

2

+

15

2

)

/

(

3

+

15

)

5

15

2

=

9

2

+

12

2

15

=

(

9

2

+

18

2

)

/

(

9

+

18

)

17

2

=

8

2

+

15

2

17

=

(

5

2

+

20

2

)

/

(

5

+

20

)

5

20

2

=

12

2

+

16

2

20

=

(

8

2

+

24

2

)

/

(

8

+

24

)

25

2

=

7

2

+

24

2

25

=

(

4

2

+

28

2

)

/

(

4

+

28

)

7

26

2

=

10

2

+

24

2

26

=

(

6

2

+

30

2

)

/

(

6

+

30

)

29

2

=

20

2

+

21

2

29

=

(

14

2

+

35

2

)

/

(

14

+

35

)

7

30

2

=

18

2

+

24

2

30

=

(

12

2

+

36

2

)

/

(

12

+

36

)

34

2

=

16

2

+

30

2

34

=

(

10

2

+

40

2

)

/

(

10

+

40

)

5

35

2

=

21

2

+

28

2

35

=

(

14

2

+

42

2

)

/

(

14

+

42

)

37

2

=

12

2

+

35

2

37

=

(

30

2

+

42

2

)

/

(

30

+

42

)

7

39

2

=

15

2

+

36

2

39

=

(

9

2

+

45

2

)

/

(

9

+

45

)

40

2

=

24

2

+

32

2

40

=

(

16

2

+

48

2

)

/

(

16

+

48

)

41

2

=

9

2

+

40

2

41

=

(

36

2

+

45

2

)

/

(

36

+

45

)

3

50

2

=

14

2

+

48

2

50

=

(

42

2

+

56

2

)

/

(

42

+

56

)

7

51

2

=

24

2

+

45

2

51

=

(

15

2

+

60

2

)

/

(

15

+

60

)

52

2

=

20

2

+

48

2

52

=

(

12

2

+

60

2

)

/

(

12

+

60

)

3

53

2

=

28

2

+

45

2

53

=

(

18

2

+

63

2

)

/

(

18

+

63

)

7

55

2

=

33

2

+

44

2

55

=

(

22

2

+

66

2

)

/

(

22

+

66

)

58

2

=

40

2

+

42

2

58

=

(

30

2

+

70

2

)

/

(

30

+

70

)

7

60

2

=

36

2

+

48

2

60

=

(

24

2

+

72

2

)

/

(

24

+

72

)

61

2

=

11

2

+

60

2

61

=

(

6

2

+

66

2

)

/

(

6

+

66

)

11

61

2

=

11

2

+

60

2

61

=

(

55

2

+

66

2

)

/

(

55

+

66

)

11

65

2

=

39

2

+

52

2

65

=

(

26

2

+

78

2

)

/

(

26

+

78

)

68

2

=

32

2

+

60

2

68

=

(

20

2

+

80

2

)

/

(

20

+

80

)

70

2

=

42

2

+

56

2

70

=

(

28

2

+

84

2

)

/

(

28

+

84

)

73

2

=

48

2

+

55

2

73

=

(

40

2

+

88

2

)

/

(

40

+

88

)

11

74

2

=

24

2

+

70

2

74

=

(

14

2

+

84

2

)

/

(

14

+

84

)

7

75

2

=

21

2

+

72

2

75

=

(

12

2

+

84

2

)

/

(

12

+

84

)

7

78

2

=

30

2

+

72

2

78

=

(

18

2

+

90

2

)

/

(

18

+

90

)

80

2

=

48

2

+

64

2

80

=

(

32

2

+

96

2

)

/

(

32

+

96

)

82

2

=

18

2

+

80

2

82

=

(

10

2

+

90

2

)

/

(

10

+

90

)

3

85

2

=

40

2

+

75

2

85

=

(

25

2

+

100

2

)

/

(

25

+

100

)

87

2

=

60

2

+

63

2

87

=

(

42

2

+

105

2

)

/

(

42

+

105

)

7

89

2

=

39

2

+

80

2

89

=

(

24

2

+

104

2

)

/

(

24

+

104

)

13

90

2

=

54

2

+

72

2

90

=

(

36

2

+

108

2

)

/

(

36

+

108

)

91

2

=

35

2

+

84

2

91

=

(

21

2

+

105

2

)

/

(

21

+

105

)

95

2

=

57

2

+

76

2

95

=

(

38

2

+

114

2

)

/

(

38

+

114

)

19

97

2

=

72

2

+

65

2

97

=

(

45

2

+

117

2

)

/

(

45

+

117

)

13

100

2

=

60

2

+

80

2

100

=

(

40

2

+

120

2

)

/

(

40

+

120

)

Title

Pythagorean hypotenuses as contraharmonic means

Canonical name

PythagoreanHypotenusesAsContraharmonicMeans

Date of creation

2013-11-20 20:23:01

Last modified on

2013-11-20 20:23:01

Owner

pahio (2872)

Last modified by

pahio (2872)

Numerical id

10

Author

pahio (2872)

Entry type

Data Structure

Classification

msc 11Z05

Classification

msc 11D45

Classification

msc 11D09

Classification

msc 11A05

Related topic

PythagoreanTriple

Related topic

ContraharmonicMean

Related topic

FirstPrimitivePythagoreanTriplets

Related topic

ContraharmonicProportion

Generated on Fri Feb 9 15:48:04 2018 by

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