Thread by @ancient_bharat

Aryabhata🙏worked on the approximation for pi (π) & come to the conclusion that π is irrational.
His work in book Aryabhatiyam📖
The ratio of the circumference to the diameter is ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures.

In the second part of the Aryabhatiyam📖,
चतुराधिकं शतमष्टगुणं द्वाषष्टिस्तथा सहस्राणाम्।अयुतद्वयस्य विष्कम्भस्यासन्नो वृत्तपरिणाहः॥
"Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."

This implies that the ratio of the circumference to the diameter is ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures.

Aryabhatta🙏

The man who changed the whole mathematics.

Aryabhatta invented zero ('0'), Calculate the value of pie ('π'), Explain the concept of Lunar-eclipse, Circumference of the Earth with 99.8% accuracy in the ancient era of (476–529 CE)🇮🇳

Trigonometry -

In Ganitapada 6, Aryabhata gives the area of a triangle as
"tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ"

that translates to:
"for a triangle, the result of a perpendicular with the half-side is the area.

Algebra -

In Aryabhatiya,

Aryabhata provided elegant results for the summation of series of squares and cubes.

Indeterminate equations -

A problem of great interest to Indian mathematicians

since ancient times has been to find integer solutions to Diophantine equations that have the form ax + by = c.

(This problem was also studied in ancient Chinese mathematics, and its solution is usually referred to as the Chinese remainder theorem.)

This is an example from Bhāskara's commentary on Aryabhatiya