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The green, leaf-shaped area below is the region of overlap between two circles of radius that are centered, respectively, at the two opposite corners of the square. What is the area of this green region?

Aryabhatta I, was born on 476 AD in Patliputra in Magadha which is now modern Patna in Bihar. He was one of the very early pioneers in astronomy and mathematics and was one of the greatest contributors in the history of mathematics. He lived in Patliputra where he wrote his famous thesis called the “Aryabhatta-Siddanta” more commonly known as the “Aryabhatiya”. This is his only work to have survived to the present day. It contains mathematical and astronomical calculations that have been discovered to be quite accurate in contemporary mathematics.

For example, he wrote that if 4 is added to 100 and then multiplied by 8 then added to 62,000 then divided by 20,000 the answer will be equal to the circumference of a circle of diameter twenty thousand. This calculates to 3.1416 close to actual value Pi (3.14159). But his greatest contribution has to be zero, known as “Shunya” in his times. His other works include theorems on trigonometry, arithmetic, algebra, quadratic equations and the sine table.

He also wrote essays on astronomy. For example he was aware that the earth spins on its axis, and that it moves round the sun and the moon rotates round the earth. He discusses about the locations of the planets in relation to its movement around the sun. Aryabhatta refers to the light of the planets and the moon as reflections from the sun. He goes as far as to explain the eclipse of the moon and the sun, day and night the contours of the earth, the light of the year exactly as 365 days.

He also calculated the circumference of the earth as 24835 miles which is close to present day calculation 24900 miles. His work was later adopted by the Greeks and then the Arabs. If one is to study the history of mathematics, Aryabhatta remains one of its greatest luminaries.