Thread by @MisraNityanand

18 ‘akshauhini’ (अक्षौहिणी) armies fought in Mahabharata war (11 on Kaurava side, 7 on Pandava side). An ‘akshauhini’ is an army with 21,870 chariots, 21,870 elephants, 65,610 horses, and 109,350 foot soldiers. If one carefully notices, one sees the mathematical relations:

1/n

21,870 = 3^7 × 10
65,610 = 3^7 × 10 × 3
109,350 = 3^7 × 10 × 5

Note the high powers of 3 (7 or 8). This is not a coincidence, all lower level of organizations of an ‘akshauhini’ were based on powers of 3, following a ternary system of counting.

2/n

Here are all the levels of organization, from the smallest to the largest, as listed in the ‘Amarakosha’:

‘patti’ (पत्ति) = 1 chariot + 1 elephant + 3 horses + 5 soldiers

‘senamukha’ (सेनामुख) = 3 ‘patti’s = 3 chariots + 3 elephants + 9 horses + 15 soldiers

3/n

‘gulm’ (गुल्म) = 3 ‘senamukha’s = 9 chariots + 9 elephants + 27 horses + 45 soldiers

‘gana’ (गण) = 3 ‘gulma’s = 27 chariots + 27 elephants + 81 horses + 135 soldiers

‘vahini’ (वाहिनी) = 3 ‘gana’s = 81 chariots + 81 elephants + 243 horses + 405 soldiers

4/n

‘pritana’ (पृतना) = 3 ‘vahini’s = 243 chariots + 243 elephants + 729 horses + 1,215 soldiers

‘chamu’ (चमू) = 3 ‘prtana’s = 729 chariots + 729 elephants + 2,187 horses + 3,645 soldiers

5/n

‘anikini’ (अनीकिनी) = 3 ‘chamu’s = 2,187 chariots + 2,187 elephants + 6,561 horses + 10,935 soldiers

Finally,

‘akshauhini’ (अक्षौहिणी) = 10 ‘anikini’s = 21,870 chariots + 21,870 elephants + 65,610 horses + 109,350 soldiers

6/n

While I am not aware of the reasons for this ternary system (I can only guess), it is clear that it was a highly mathematical organization. Such was ancient India, with mathematics followed in almost every sphere of life, including organization of armies.

n/n