Thread by @KS1729

since it is the christmas holidays, something fun:

here is a Sanskrit verse from 15thC Kerala in south India by a mathematician Madhava (~1360-1420)

vibudhanetragajaahihutaasanatrigunavedabhavaarannabaahavah I
navanikharvamite vrrtivistare paridhimaanam idam jagadur budhaah ||

what does this mean?

"Gods, eyes, elephants, snakes, fires, three, qualities, Vedas, the constellations, elephants, and arms -- the wise say that this is of the circumference when the diameter of a circle is nine hundred billion."

a while ago, i had tweeted a thread about the Katapayadi system [if interested see here:

https://twitter.com/KS1729/status/1172858719199277057

]

lesser known is the 'bhootasankhya' system -- which refers to the 'bhootanam sankhya' or 'numbers linked to (spectral?) beings'

What this system does is it takes specific types of phenomena/structures/beings that are commonly known and used in Sanskrit literature and associates numbers with it.

For e.g.,

The number 1 is associated with Sun, Moon, planets, mountain, sky etc

Number -- Bhoota referred

0 -- kham, aakasha,... all synonyms of sky/space
1 -- indu, chandra, sasadhara... [moon]
-- prthvi, vasundhara, dhara... [earth]
2 --aksi, cakshu, netra... [eyes]
3 -- agni, vahini... [fire]
.
.
24 -- arhat, gayatri
48 -- jagati (meters)

& so on

Knowing this schemata of translation (phrases --> words), you can hide numbers in plain sight. For eg., the phrase 'vedavedangachandra' is [4][4][9][1] is flipped to get 1944.

Unlike the katapayadi schema, this allows you the freedom to rhyme and fit into meter as well.

Before we get back to Madhava's verse:

Madhava seems to have taken astronomy seriously -- like Copernicus (1473-1543) who was his contemporary -- and improvised/tinkered with a tradition that came down to him. But he was more 'mathematical'

One of Madhava's remarkable verses:

"Multiply the diameter by 4, divide by 1. Apply separately with -ve and +ve signs alternately the product of the diameter and 4 divided by odd numbers 3, 5, & so on...The result is the accurate circumference; it is extremely accurate if the division is carried out many"

This, in our notation, becomes:

C = 4D/1 - 4D/3 + 4D/5 - 4D/7 +...

which we learn is the same as the infinite series formula of pi. Something we attribute to Leibnitz (1646-1716). See the summary here:

Now let's go back to Madhava's verse & combine it with the Bhootasankhya system

"Gods[33], eyes[2], elephants[8], snakes[8], fires[3], three[3], qualities[3], Vedas[4], constellations [27], elephants[8], and arms[2] - the wise say...diameter of a circle is nine hundred billion."

This, when written out becomes:

= (2827433388233/900000000000)
= 3.141592654
[the value of pi correct to the 11th decimal place!]

[all of the above is courtesy the pioneering works of K. V. Sarma, David Pingree, K.S. Shukla, K. Ramasubramaniam, M. S. Sriram, R.C. Gupta]