Nilakantha Somayaji's Work on Calculus and Infinite Series
Nilakantha Somayaji was an Indian mathematician and astronomer who lived in the 15th century. He is best known for his work on calculus and infinite series, which was published in his book Tantrasamgraha. This quiz will test your knowledge of Nilakantha Somayaji's work on calculus and infinite series.
Questions
In which book did Nilakantha Somayaji publish his work on calculus and infinite series?
- Tantrasamgraha
- Aryabhatiya
- Lilavati
- Siddhanta Shiromani
What is the name of the series that Nilakantha Somayaji used to calculate the value of pi?
- Gregory-Leibniz series
- Taylor series
- Maclaurin series
- Nilakantha series
What is the formula for the Nilakantha series?
- $$\pi = 3 + \frac{4}{2 \cdot 3 \cdot 4} - \frac{4}{4 \cdot 5 \cdot 6} + \frac{4}{6 \cdot 7 \cdot 8} - \cdots$$
- $$\pi = 4 - \frac{4}{2 \cdot 3} + \frac{4}{4 \cdot 5} - \frac{4}{6 \cdot 7} + \cdots$$
- $$\pi = 3 + \frac{4}{2 \cdot 3} + \frac{4}{4 \cdot 5} + \frac{4}{6 \cdot 7} + \cdots$$
- $$\pi = 4 - \frac{4}{2 \cdot 3 \cdot 4} + \frac{4}{4 \cdot 5 \cdot 6} - \frac{4}{6 \cdot 7 \cdot 8} + \cdots$$
What is the value of pi that Nilakantha Somayaji calculated using the Nilakantha series?
- 3.14159265
- 3.141592653589793
- 3.1415926535897932384626433832795
- 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
What is the name of the method that Nilakantha Somayaji used to find the derivative of a function?
- Newton's method
- Leibniz's method
- Rolle's method
- Nilakantha's method
What is the formula for Nilakantha's method for finding the derivative of a function?
- $$f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$$
- $$f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x - h)}{2h}$$
- $$f'(x) = \lim_{h \to 0} \frac{f(x + h) + f(x - h)}{2h}$$
- $$f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{2h}$$
What is the name of the series that Nilakantha Somayaji used to find the sum of an infinite series?
- Gregory-Leibniz series
- Taylor series
- Maclaurin series
- Nilakantha series
What is the formula for the Nilakantha series for finding the sum of an infinite series?
- $$S = \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n}$$
- $$S = \sum_{n=1}^\infty \frac{1}{n}$$
- $$S = \sum_{n=1}^\infty \frac{1}{n^2}$$
- $$S = \sum_{n=1}^\infty \frac{(-1)^n}{n}$$
What is the sum of the infinite series $$S = \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n}$$?
- 0
- 1
- $\frac{1}{2}$
- $\frac{1}{4}$
What is the name of the method that Nilakantha Somayaji used to find the area of a circle?
- Gregory-Leibniz method
- Taylor method
- Maclaurin method
- Nilakantha method
What is the formula for the Nilakantha method for finding the area of a circle?
- $$A = \pi r^2$$
- $$A = 2\pi r$$
- $$A = \frac{1}{2}\pi r^2$$
- $$A = \frac{1}{4}\pi r^2$$
What is the area of a circle with radius 10 units?
- 100\pi
- 200\pi
- 300\pi
- 400\pi
What is the name of the method that Nilakantha Somayaji used to find the volume of a sphere?
- Gregory-Leibniz method
- Taylor method
- Maclaurin method
- Nilakantha method
What is the formula for the Nilakantha method for finding the volume of a sphere?
- $$V = \frac{4}{3}\pi r^3$$
- $$V = \frac{1}{3}\pi r^3$$
- $$V = \frac{2}{3}\pi r^3$$
- $$V = \frac{3}{4}\pi r^3$$
What is the volume of a sphere with radius 10 units?
- 4000\pi
- 8000\pi
- 12000\pi
- 16000\pi