Contributor: Archimedes of Syracuse
Time Period: 3rd century BCE
Location: Ancient Greece
Description: Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter. It is an irrational number, meaning it cannot be expressed as a simple fraction, and its decimal representation goes on infinitely without repeating. Pi is approximately equal to 3.14159 and is used extensively in mathematics, physics, engineering, and various other fields.
“Archimedes stated that not the exact but the value of PI (π) lies somewhere between 3 1/7 and 3 10/71.”

Archimedes of Syracuse

Inventor: Acharya Aryabhatt (Expert Mathematician and Scholar of Astronomy)
Time Period: 5th century CE
Location: Bharatvarsh

Description: Acharya Aryabhatt was an ancient Indian mathematician and astronomer who made significant contributions to the field of mathematics. In his work "Aryabhatiya," he presented the most appropriate value of π that is 3.1415… which is followed and considered by the world till the present day. Acharya Aryabhatt discussed various mathematical concepts related to geometry and trigonometry.

Evidence:

Aryabhatiya, an ancient Indian mathematical and astronomical treatise, does provide an approximation for the value of π (pi) in one of its verses. Here are the relevant verses:

Aryabhattiya, Ganita Pada, Verse 10:

चतुरधिकं शतमष्टगुणं द्वाषष्टिस्तथा सहस्त्राणाम्।

अयुतद्वयविष्कम्भस्यासन्नो वृत्तपरिणाहः ॥ १० ॥

Meaning: 100 added 4, multiplied by 8 and added 62,000, this is the circumference of a circle whose diameter is 20,000.
Aryabhatiya, Ganitapada, Verse 3.14:

गोपीभाग्य मधुव्रातः शृङ्गिशोदधिसंधिगः।

सखी लेक्षणसंस्था सशरीर मुक्तयः।

विभाग चक्रवाले शृङ्गिर्यंत्रे शब्दयोजने।

द्वादशाध्यायिका स्थिरास्त्रिंशद्द्वादशाक्षरा।। 3.14 ।।

Meaning: "The circle of the zodiac, bhagya (portion of fortune), the daily motion of the moon, the intercalary lunar month, and the intercalary year have 32 parts. In a circle with 360 degrees, Acharya Aryabhatt divides the circumference into 24,000 parts, and this is the value he gives for π (pi), which is approximately 3.1416."

Connection between Modern and Ancient Concept:

The contributions of ancient scientists and Mathematicians like Acharya Aryabhatt continuously help the modern Mathematics in its discoveries and calculations. This shows how intellectual, skilled and educated they were at those times and were able to do such complex experiments which are the roots of the modern mathematics till date. Despite being from different regions and time periods, both Aryabhatt and Archimedes made significant contributions to the development of mathematical concepts, including the understanding of π.

Conclusion:

Acharya Aryabhatt was a great astronomer and Mathematician who made huge and very important contributions to the Space Science and Mathematics. The modern science and Mathematics is the result of the excellent contributions which were made by the Ancient experts. They continue to inspire the modern era with their mind blowing inventions and discoveries. Both Aryabhatt's work and Archimedes' contributions exemplify the timeless pursuit of mathematical knowledge across different civilizations and epochs.