The Pythagoras Theorem

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3 Step Vedic Way to Solve Pythagoras Theorem

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The Pythagoras Theorem

  1. 1. THE PYTHAGORAS THEOREM 3 Easy Vedic Steps to find the other two sides, given 1 side of a right angled triangle.
  2. 2. The Pythagoras theorem was invented by Pythagoras. Pythagoras (ca. 582 - ca 497 B.C.) was a Greek philosopher and mathematician. Pythagoras' ideas influenced great thinkers throughout the ages. Pythagoras is well known to math students for the Pythagoras theorem. Background
  3. 3. Pythagoras theorem is a simple rule about the proportion of the sides of right triangles. The Pythagoras theorem states that: “ the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides of the right triangle.” Or simply put – c 2 =a 2 + b 2 Background
  4. 4. However the basics and practical utility of this theorem was known to the ancient Indians long ago when the western mathematicians were in the primitive stage. The proof of this theorem as given by the westerners is tedious whereas there are many easy Vedic proofs . However we go straight to the application of finding the two sides given one side of a Right Angled Triangle. Background
  5. 5. Lets take one side of the right angled triangle to be 8 cm Our objective to find the other 2 sides. Example 1
  6. 6. Step 1 : Find Square of 8 = 64
  7. 7. Step 2 : Find the factors of 64. They are 64,32,16,8,4,2 and 1. Now depending on these factors, there will be various triangles.
  8. 8. Step 3 : Lets take 32. Now 32 x 2 = 64. So we substitute for x = 32 & y = 2 in the formula (x+y) and (x-y) 2 2 And we get our sides. So we get 32+2 = 17 and 32-2 = 15 2 2 Therefore 8,17 and 15 is one right angled triangle. Lets find the other sets.
  9. 9. Factors of 64 Application of formula Our sides in cm 64 x 1 = 64 a) 8,31.5 and 32.5 16 x 4 = 64 b) 8,6 and 10 8 x 8 = 64 c) No triangle Thus we get 3 Right Angled triangles where one side is 8cms. Easy isn't it? 64+1=32.5& 64-1= 31.5 2 2 16+4 = 10 & 16-4 = 6 2 2 8+8 =8 & 8-8 = 0 2 2
  10. 10. Lets take one side of the right angled triangle to be 7cm Our objective to find the other 2 sides. Example 2
  11. 11. Step 1 : Find Square of 7 = 49
  12. 12. Step 2 : Find the factors of 49. They are 49,7 and 1. Now depending on these factors, there will be various triangles.
  13. 13. Factors of 49 Application of formula Our sides in cm 49 x 1 = 49 a) 7,24 and 25 7 x 7= 49 b) No triangle Thus we get only one Right Angled triangle whose one side is 7cms. Could it be easier? 49+1=25 & 49-1=24 2 2 7+7 =7 & 7-7 =0 2 2
  14. 14. Now try with any number as one side of the right angled triangle.

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