### Concept of Pythagorean Theorem's New Proofand Pythagorean's Triple With Ancient Vedic Investigation

#### Abstract

“In a Right-Angle Triangle the sum of the Areas of Semi circles (Half -circles) formed on the two sides is equals to the Area of the semi circle (Half circle) formed on the hypotenuse.”

Area of a circle = (where r is radius of the circle)

Area of a semi circle (Half-Circle) = OR

= (Where 'D' is diameter of the circle)

Semi-circles Area of two legs (a and b) = +

= +

= +

= (a^{2}+b^{2}) Sq. Units………….(1)

Now Area of the long leg c is Semi Circle (Half -Circle)

Area of the Long Leg (Hypotenuse) =

=

= Sq. Units……….(2)

From (1) and (2)

They are equal i.e. (1)=(2)

(a^{2}+b^{2}) =

a^{2}+b^{2} = c^{2} ………..........................................(3)

[Dividing both sides by ]

This is Pythagoras (Pythagorean) Theorem.

In the Mantra of Gunia, Vishavakarma Ji gave the Triple before the Pythagoras and other ancient Philosopher.

Mantra of Gunia is:

nON rwj bwrW rws pMdrW

iqb ibTwvy rws bno sUq[

qb AKvwvy ivSvkrmw kw pUq

{Nau Raj Barah Ras Pandrah,

Tab Bithawe Ras bano Sut (Thread)

Then will be say to son of Vishavkarma}

*Vishavakarma’s Triple is*

*(9, 12, 15)*

Right angle Triangle (i.e. Gunia) is formed only when there are Vishavakarma’s Triple i.e. (9, 12, 15)

And its prime Triple is formed dividing by 3 i.e. (3,4,5) when ever the proof of this theorem is not discovered at that time. But these triple is same as Pythagorean Triple (3n, 4n, 5n) i.e. = where is any multiple of this triple. These are also related to the Babylonians Triple who discovered Algebraically between 2000 and 1786 BC. The middle Egyptian kingdom.

So, we can say that Triple was discovered by Vishavakarma although Right Angle triangle does not mentioned in it.

#### Full Text:

PDF#### References

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(Bhagwan Vishvakarma Ji)

Jagjit Singh Komal, Hoshiarpur

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