(a+b)2 = a2 + b2 + 2ab: This is how mathematics should be taught

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  Ramani Aswath

  The Maharashtrian mathematecian Bhaskara II gave an interesting algebraic proof of the pythagorean Theorem:
  Proof #4
  
  The fourth approach starts with the same four triangles, except that, this time, they combine to form a square with the side (a + b) and a hole with the side c. We can compute the area of the big square in two ways. Thus
  (a + b)² = 4·ab/2 + c²
  simplifying which we get the needed identity.
  A proof which combines this with Pythagorean Theorem and its many proofs is credited to the 12th century Hindu mathematician Bhaskara (Bhaskara II):
  
  Here we add the two identities
  c² = (a - b)² + 4·ab/2 and
  c² = (a + b)² - 4·ab/2
  which gives
  2c² = 2a² + 2b².
  The latter needs only be divided by 2.
  
  Pythagorean Theorem and its many proofs
  
  TEachers must make it interesting to students.