MATHS IN HINDUISM – I
The oldest civilization in the world, the Indian Civilization was a storehouse of discoveries. It wouldn’t be wrong to call our ancient Rishis as Scientists. The many, many discoveries they made about this world still amaze the scientists of today. These discoveries are in the field of Maths, Astronomy, Metallurgy, Astrology, Music, Dance, Philosophy, Medicine, Spirituality and more. We Hindus had this unique way of recording these discoveries in the form of Shlokas or Stotras (hymns in a poetry form), using simple or complex words, in Sanskrit – the language of that generation. Because they were coded in this form, a lot of these discoveries remained hidden from the modern world and it is only now that we are rediscovering them, especially in the last 50-100 years. As I said in my previous blog on Hinduism, the invaders not just looted our country, they also destroyed many valuable works and these are lost forever.
Before we talk about our ancient discoveries, it is important that one realizes and venerates our ancient Rishis for sharing this knowledge FREELY, with only the expectation that everyone becomes more and more knowledgeable and use this knowledge to reach out to the Supreme One – Brahman. Such selflessness and generosity was what our India was known for. We never patented or earned from our discoveries & while this might seem to be foolishness to some, this was the reason why our Sanatan Dharm still exists while others have been lost in the sands of time. Now onwards to Maths – Please note that I will not be talking about the Zero or the Decimal System or the Anu (Atom), which by now almost all Indians know about and are proud about …
CALCULATING SQUARES and SQUARE-ROOTS: The Shri Rudra Hymn and the Chamaka are part of the Yajur Veda and it is dedicated to Lord Shiva. It is in the Chamaka that one learns about the Squares and the Square-Roots. The Chamaka has the following verses:
Eka Chame, Trisra Chame, Pancha Chame …. Nava Ving Satis Chame, Eka Triyam Satis Chame
Now let us see what they mean –
Eka (one) Chame 01+000 = 001 its root is 01
Trisra (three) Chame 03+001 = 004 its root is 02
Pancha (five) Chame 05+004 = 009 its root is 03
Sapta (seven) Chame 07+009 = 016 its root is 04
Nava (nine) Chame 09+016 = 025 its root is 05
Sapta Ving Satis (27) Chame 27+169 = 196 its root is 14
Nava Ving Satis (29) Chame 29+196 = 225 its root is 15
Eka Triyam Satis (31) Chame 31+225 = 256 its root is 16
The Yajur Veda is one of the Four Vedas that we call Shruti – the word of God. The others are Rig Veda, Saama Veda and Atharva Veda. Their date of origin is not known – in fact we believe that there is no date of origin at all. It is timeless. From the above, it is obvious that our Rishis knew numbers, odd and even, multiplication and division and roots and squares. But because they thought that this was wisdom which was part of creation itself, of Para Brahman, they included it in holy texts. Readers would be interested in knowing that the Vedas have verses attributed to the sages who visualized them during their meditation. These verses are part of the Divine knowledge and so are called Shruti.
FIBONACCI NUMBER SERIES & RATIO: It is Pingala who is credited with the discovery of the Fibonacchi sequence. He has written about this in his book Chandahsastra. In simple language ‘Chandah’ is the meter used for writing verses in Sanskrit. This means that one could use a certain number of syllables with a certain number of verses to write a Shloka – for eg. a Gayatri Chandah has 3 verses with 8 syllables, a Anushtubh Chandah has 4 verses of 8 syllables, etc. Using these Chandah in a way to grant certain energies was a unique form of writing in ancient India. Fibonacci Sequence – Matrameru – Matra – a unit of metrical quantity equal to a short vowel in Sanskrit and other Indian languages & Meru – Mountain. This is how it looks:
The above structure shows us the Fibonacci sequence – 1,1,2,3,5,8,13 …when you go cross-wise . Readers would also be interested in knowing that our Rishis believed that what was in us is what was outside of us. That is one of the reasons the Human Birth was considered the ultimate (Shreshth Yoni). The Fibonacci series appears in our body too. 1 palm, 1 thumb on each palm, 2 thumbs, 3 bones on each digit, 5 fingers on each palm, 8 digits… The Fibonacci ratio or the Golden Ratio is 1:1.618. The ratio between the first two bones of each digit (finger) is 1:1.618 & the ratio between the next two bones on each digit is the same. The ratio from the navel to your head & from the navel to the bottom of your feet is also 1:1.618 (Now you know why in Bharat Natyam, the dancer bends her legs at her knees and dances- to make the body length equal). Trees & their branches, leaves all follow the Fibonacci sequence. It is a known fact that our Jyotirlings (Shiva Temples) are constructed in the Fibonacci sequence.
… to be continued