650 BC, but we are not sure: Soldiers barge in the school, making the teacher angry; and when they take him prisoner, the anger breaks free. "This is a temple of learning; you cannot bring weapons in here. What have I done?" asks the teacher.

"You have been accused of treason and corrupting the youth, disobeying orders of the king and defying the authority of the royal priest," soldiers tell him.

"I didn’t know I had done all this; seems to be quite a damage for one person to do."

The priest is brought in chains to the palace, where Manava, royal priest and author of one of the Sulbasutras, priceless works of mathematics, is making offerings to the Gods for the king. He is a man of considerable learning, but not interested in mathematics for its own sake, only in using it for religious purposes. He wrote the Sulbasutra to give rules for religious rites, to enable accurate construction of altars for sacrifices.

Manava’s Sulbasutra, like all the Sulbasutras, contains approximate constructions of circles from rectangles, and squares from circles. Every construction involving circles leads to a different such approximation, so there are several inaccuracies.

"You been teaching your students how to challenge my theories," says Manava.

"Sir, I have only been teaching them how to think and they, on their own, have learnt to extend your theories," the teacher says.

Manava: "My theories are not rubber, these cannot be extended. Your arguments are paradoxical."

"Perhaps, the greatest paradox of all is that there are paradoxes in mathematics," says the teacher.

"Give the royal priest your toughest problem and, if he solves it, it shall be a big problem for you," says the king.

Teacher: "There exists a city surrounded by a circular wall. The wall has two gates, one on the north end and one on the south end. A yellow house stands 3 miles north of the north gate. A blue house stands 9 miles east of the south gate. The yellow and blue houses can barely see other around the side of the wall. What is the radius of the circle formed by the wall?"

Though Manava is able to solve the problem in his mind, he remains silent; and the teacher wins his freedom. Manava turns to serious study of mathematics.

What was the answer and why did Manava remain silent? Write at Mind Games, Windows, The Tribune or adityarishi99@yahoo.co.in.

— Aditya Rishi