Saturday, 9 September 2017

Was pi really invented in India?

Wikipedia says that pi was invented by William Jones, a mathematician from Wales, in the 1970s. But, little do we know that our own legendary mathematician Aryabhatta had mentioned the value of pi in one of his ancient shloks, written in 455 A.D.

Our ancestors had a very unique way of passing their time in those days. Most of their time was spent in doing yagnas to various demigods and goddesses. One of the peculiar features of the yagnakundas used for doing yagna was their unique shapes. Some yagnakundas were square, some were circle and some semi circle. The area of the yagnakunda, however, was same for all yagnakundas.

Now, a simple mathematical equation, as given below, between the area of square and circle, can give us the radius of a circle whose area is equal to a given square.

But, how did the ancient Indians build yagnakundas of same area and different shapes? The following shlok written by Aryabhatta in 455 A.D. gives us an idea of how the ancient Indians might have been able to design such intricate structures:

chaturadhikaM shatamaShTaguNaM                    dvAShaShTistathA sahasrANAm AyutadvayaviShkambhasyAsanno vr^ttapariNahaH
          [gaNita pAda, 10] Aryabhatiyam (499 CE) 

Chatur-4, adhikam-add, shatam-100, ashta-8, gunam-multiply, dwashashtistatha sahasranam-62000, ayuta-divide, dwayavishkambha-20,000, Asanno-approximate;

The above shlok, in short, means:
“Add 4 to 100, multiply by 8 and add to 62,000. This is approximately the circumference of a circle whose diameter is 20,000.” 
                            i.e. \pi \approx \frac{62,832}{20,000} = 3.1416 
               correct to four places.
The word "Asanna" indicates that this is an approximation. 

This value was used to build yagnakundas of circular shapes.

Does this mean that Aryabhatta was the true inventor of pi?