Alternate Pythagoras Theorem

9

We have learnt Pythagoras Theorem in our lower classes which states that “the hypotenuse side is equal to the square root of the sum of the squares of Parajumpers Men the opposite side and adjacent side“.
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This can be stated as

a^2 + b^2 = c^2\!\,

where

c-Hypotenuse side

a and b- the other two sides(opposite,adjacent)

Here we have to take the square root of c² to find the hypotenuse side.

 c = \sqrt{a^2 + b^2}. \,

The alternate method of Pythagoras theorem has been found in a Tamil Poem.

It was found by Bodhaiyannaar. The concept is

Method 1:

1. Among the opposite side and the adjacent side pick the greater number and divide it by 8.

2. Then subtract the result from the same.

3.Now divide the smaller number by 2.

4.Now add these both and the hypotenuse side will be obtained.

 

The actual English translation of the poem is “Divide the distance you’ve run (longer side) into 8 equal parts and discard one part from it. Then if you add the half the height to that, you’ll get Hypotenuse.” Parajumpers Men

Method 2:

Now as per the poem, Hypotenuse = (7/8)*7 + 6/2 = 10.

Now see in this case

Hypotenuse = (7/8)*6 + 3/2 = 6.75

And when you go by Pythagoras theorem you would be obtaining an answer of 6.71.

So we can either multiply the bigger number with 7/8 and proceed or subtract it with the same divided by 8 and proceed.

Unlike Pythagoras theorem – where you need to find the square root of the result, this theorem can be computed with basic mathematical operations,which reduces the complexity of the problem.

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9 Comments

  1. Mathematician :

    Nice idea, but unfortunately … wrong.

    Counterexample:

    a = 4, b = 4, correct pythagorean hypotenuse = sqrt(32) = 5.656854….

    By your rule, hypotenuse should be 4*(7/8) + 4/2 = 5.5, which is wrong.

    Note that square roots are often irrational numbers, unless they happen to be taken from a square. You cannot produce an irrational number by operations with fractions (the rational numbers are a field, and addition, multiplication and division cannot lead you outside of it).

    We’re looking at the beauty of mathematics here and not the exactness of the answer.

  2. mani_bharathi on

    @Logic Induction
    For bigger numbers calculating the square root manually is difficult.Pythagoras theorem is mostly employed in school level where students wont be allowed to use calculator.In that case this theorem would be useful to compute for larger numbers.

  3. @Mathematician
    Well i dint mean to prove that both are same.My point is that there is an alternative way to find hypotenuse side without applying Pythagoras theorem.I agree with you that it varies with decimal point.But still we are able to find the hypotenuse side approximately.

  4. Logic Induction on

    Interesting from a theoretical point of view.

    Pythagoras theorem and its expression is rather elegant. Why is a square root more difficult ?

  5. Mathematician on

    Nice idea, but unfortunately … wrong.

    Counterexample:

    a = 4, b = 4, correct pythagorean hypotenuse = sqrt(32) = 5.656854….

    By your rule, hypotenuse should be 4*(7/8) + 4/2 = 5.5, which is wrong.

    Note that square roots are often irrational numbers, unless they happen to be taken from a square. You cannot produce an irrational number by operations with fractions (the rational numbers are a field, and addition, multiplication and division cannot lead you outside of it).