Curiously the quadratic formula is known in Brazil as Bhaskaras formula. Turns out the Portuguese started translating Indian texts from 1519 and took it to Europe and the new world. Over the next 200 years, all manner of mathematical, medical and philosophical concepts boom in Europe, which for some reason are also in Indian texts.
Interestingly multiple scholars invent the same science around the same time unknown to each other like Calculus.
Nah... that is not even the best part. Here is the real FUN FACT:
In the Aryabhatiya (Ganitapada, Verse 21), written in 499 CE, Aryabhata introduces the mathematics of stacking. He explicitly lays out the formula for finding the total number of items in a pyramid pile with a triangular/square base. For a pyramid stack where each side of the base has 'n' spheres:
Total Spheres = [ n ร (n 1) ร (n 2) ] / 6
Think about the timeline here. Johannes Kepler conjectured that this layout was the densest in 1611. Aryabhata had already mapped out the exact algebraic discrete-volume matrix to count every single individual sphere within that dense packing formation 1000s yrs earlier.
Fun Fact is still not over. Fast-forward to the 12th century. The legendary mathematician Bhaskara II takes Aryabhataโs foundation & elevates it into a poetic, highly advanced art form in his textbook, the Lilavati. Bhaskara creates a dedicated mathematical category called Citi-Ghana (the volume of a pile). He did not just give 1 formula; he realized that different stacking bases create different geometric properties. He breaks down eqns for:
- Triangular-based pyramids (where spheres rest in the gaps of a triangular grid)
- Square-based pyramids (the standard grocery-stack style)
- Oblong piles (where the base is a rectangle)
To solve these, Bhaskara had to utilize Varga-Sankalita (the sum of squares of natural numbers) & Ghana-Sankalita (the sum of cubes). While Western mathematics at the time was struggling with basic arithmetic using Roman numerals, Indian scholars were utilizing advanced series expansions to handle the discrete boundaries of 3 dimensional sphere packing.
Now the Fun Fact is over ๐๐