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Published on January 12th, 2011 In category Education | Geometry | Maths

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Pythagorean triplets

A pythogrean triplet is a set of 3 number say x, y z such that x2 + y2 = z2

Here are some triplet number set that satiesfies the condition stated by Pythagorean theorem, it is important to byheart these numbers as it will help to solve many type of problems very easily

The triplet with z > 100 are as follows:

( 3 , 4 , 5 )              ( 5, 12, 13)            ( 7, 24, 25)           ( 8, 15, 17)

( 9, 40, 41)            (11, 60, 61)          (12, 35, 37)          (13, 84, 85)

(16, 63, 65)           (20, 21, 29)          (28, 45, 53)          (33, 56, 65)

(36, 77, 85)          (39, 80, 89)          (48, 55, 73)          (65, 72, 97)

How can be these sets be used?

  • If x, y z are Pythagorean triplets

 

 

  • (z- x)(z-y)/2 is a perfect square always, this would be helpful in solving problems
  • Only one of x, y or Z can be square number

The pythogoreaus theorm can also be used for

         
   The radius of the inscribed circle is given as                

 If only r is given then  we can find out x = 2r + 1, y =  2r(2r+1)  and z =  2r(2r+1) +1

 

 

Divisibility Rules for Pythagoras Triplets

  • Exactly one of x, y is odd; z is odd.
  • Exactly one of x, y is divisible by 3.  (check out earlier post: how to easily divide by 3, 6 or 9)
  • Exactly one of x, y is divisible by 4.  (check out earlier post: how to easily divide by 4 or 8, )
  • Exactly one of x, y, z is divisible by 5.
  • Exactly one of x, y, (x + y), (x − y) is divisible by 7.  (check out earlier post: how to easily divide by 7)
  • Exactly one of (x + z), (y + z), (z − x), (z − y) is divisible by 8.  
  • Exactly one of (x + z), (y + z), (z − x), (z − x) is divisible by 9.  
  • Exactly one of x, y, (2y + x), (2y − x), (2x + y), (2x − y) is divisible by 11.  (check out earlier post: divisible by 11)

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