// minds behind maths
Pingala
c. 300 BCE · Combinatorics, prosody
Author of the Chandahshastra, a treatise on Sanskrit prosody. In analysing the patterns of short and long syllables in poetic metre, Pingala described a binary representation of numbers and related combinatorial structures — ideas that prefigure the binary system underlying modern computing. As later elaborated by his 10th-century commentator Halayudha, Pingala's method of counting these patterns forms the Meru-prastara (the 'Staircase of Mount Meru') — the array of binomial coefficients now widely known as Pascal's triangle, which gives the coefficients in the cube and binomial expansions in the algebra section.
Source: Wikipedia — Pascal's triangle
Formulas that trace back to Pingala
Cube of (a−b−c)
(a-b-c)³
Cube of a Difference (a−b)³
(a-b)³ = a³ - 3a² b + 3ab² - b³
Cube of a Linear Binomial (ax+b)³
(ax+b)³ = a³x³ + 3a²bx² + 3ab²x + b³
Cube of a Sum (a+b)³
(a+b)³ = a³ + 3a² b + 3ab² + b³
Cube of a Trinomial (a+b+c)³
(a+b+c)³ = a³+b³+c³+3(a+b)(b+c)(c+a)
Difference (a+b)³ − (a−b)³
(a+b)³ - (a-b)³ = 6a² b + 2b³
Pascal Terrain
binomial coefficients as a 3D terrain
Sum (a+b)³ + (a−b)³
(a+b)³ + (a-b)³ = 2a³ + 6ab²