Do You Know Madhava Series?

Explanation
Madhava of Sangamagrama is from Sangamagrama.

Explanation
The number of Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159.

Explanation
Madhava obtained a value for Pi with 13 decimal places. This means that he calculated Pi accurately up to the thirteenth decimal place.

Explanation
Madhava has composed an accurate table of sines. This means that he has created a comprehensive and precise chart that displays the values of the sine function for various angles. Such a table would be useful in various mathematical and scientific calculations involving trigonometry, enabling accurate calculations and measurements in fields such as physics, engineering, and astronomy.

Explanation
None of Madhava's works containing any of the series expressions attributed to him have survived.

Explanation
James Gregory is the correct answer because he is the one who rediscovered the Madhava series. The Madhava series, also known as the Kerala school series, is a mathematical series that was originally developed by the Indian mathematician Madhava of Sangamagrama in the 14th century. However, the series was lost and forgotten over time. It was James Gregory, a Scottish mathematician, who rediscovered and brought attention to the series in the 17th century. Gregory's rediscovery of the Madhava series played a crucial role in the development of calculus and the expansion of mathematical knowledge.

Explanation
James Gregory rediscovered Madhava series in 1668.

Explanation
Madhava laid the foundations for the study of Calculus. Calculus is a branch of mathematics that deals with the study of change and motion. It includes concepts such as limits, derivatives, and integrals. Madhava, an Indian mathematician and astronomer, made significant contributions to the development of Calculus in the 14th century. He is known for his work on infinite series and the discovery of the power series representation of trigonometric functions. Madhava's contributions laid the groundwork for the later development of Calculus by European mathematicians such as Isaac Newton and Gottfried Wilhelm Leibniz.

Explanation
Madhava was born in the 14th century. This can be inferred from the given options, where the 14th century is the only century listed among the choices.