Geometry in Indian mathematics

Pythagoras Theorem

• The Pythagoras Theorem, which states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse, was known in India as the Bhuja-koti-karna-nyaya.
• This theorem is described in the Baudhayana-sulba-sutra, an ancient Indian mathematical text.

Shadow Problem

• Indian mathematical works contain interesting problems of day-to-day importance solved using mathematical principles.
• One such problem is the shadow problem, which involves finding the length of the shadow cast by a lamp post or a stick.
• The solution to this problem involves using similar triangles and their properties.
• This problem has an equivalence in astronomy, where the sun, earth, and moon are considered instead of the lamp post, stick, and shadow.

Value of π (pi)

• The value of π is important in geometry and has been approximated by Indian mathematicians since ancient times.
• Aryabhata gave an approximation of π as 3.1416 in the 5th century CE.
• Madhavacharya, in the 14th century CE, discovered several infinite series for π, which were later rediscovered by European mathematicians.
• Madhavacharya also gave a technique for finding better approximations for π using correction terms in the series.
• He estimated the value of π accurate to 11 decimal places.

History of π Approximation in India

• The table below summarizes the history of π approximation by Indian mathematicians:

Conclusion

Indian mathematicians made significant contributions to geometry, including the Pythagoras Theorem, the shadow problem, and the approximation of π. Their work demonstrates a deep understanding of geometric principles and their application to real-world problems.