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:
| Mathematician/Text | Date | Approximation | Accuracy | Method |
|---|---|---|---|---|
| Sulba-sutras | 800 BCE | 3.08888 | 1 decimal place | Geometrical |
| Jaina texts | 500 BCE | 3.1623 | 1 decimal place | Geometrical |
| Aryabhata | 499 CE | 3.1416 | 4 decimal places | Polygon doubling |
| Bhaskaracharya | 1150 CE | 3927/1250 | 4 decimal places | Polygon doubling |
| Madhavacharya | 14th century CE | 3.14159265359222 | 11 decimal places | Infinite series |
| Ramanujan | 1914 CE | - | 17 million digits | Modular equation |
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.