The arithmetic class was in progress. The teacher was solving questions on division. On the blackboard were drawn three bananas. "We have three bananas, " the teacher said, "and we have three boys.Can you tell me how many each will get?"
A smart boy in the front row replied, "Each will get one."
"Right, " the teacher said. "Now, similarly, if 1,000 i bananas are distributed among 1,000 boys, each will get one, Isn't that so?"
While the teacher was explaining, a boy sitting in one corner raised his hand and stood up. The teacher stopped and waited for the boy to speak.
"Sir, " the boy asked, "if no banana is distributed among no one, will everyone still get one banana?" There was a roar of laughter in the class. What a silly question to ask!
"Quiet," the teacher said loudly and thumped the desk. "There's nothing to laugh at. I will just explain what he means to say. For the division of bananas, we divided three by three, saying that each boy will get one banana. Similarly, we divided 1,000 by 1,000 to get one. What he is asking is that if zero banana is divided among zero, will each one get one? The answer is 'no'. Mathematically, each will get an infinite number of bananas!"
Everyone laughed again. The boys understood the trick arithmetic had played upon them. What they could not understand was why the teacher later complimented the boy who had asked that absurd question.
The boy had asked a question that had taken mathematicians several centuries to answer. Some mathematicians claimed that zero divided by zero was zero. Others claimed it to be unity. It was the Indian mathematician Bhaskara who proved that it is indeterminate.
A smart boy in the front row replied, "Each will get one."
"Right, " the teacher said. "Now, similarly, if 1,000 i bananas are distributed among 1,000 boys, each will get one, Isn't that so?"
While the teacher was explaining, a boy sitting in one corner raised his hand and stood up. The teacher stopped and waited for the boy to speak.
"Sir, " the boy asked, "if no banana is distributed among no one, will everyone still get one banana?" There was a roar of laughter in the class. What a silly question to ask!
"Quiet," the teacher said loudly and thumped the desk. "There's nothing to laugh at. I will just explain what he means to say. For the division of bananas, we divided three by three, saying that each boy will get one banana. Similarly, we divided 1,000 by 1,000 to get one. What he is asking is that if zero banana is divided among zero, will each one get one? The answer is 'no'. Mathematically, each will get an infinite number of bananas!"
Everyone laughed again. The boys understood the trick arithmetic had played upon them. What they could not understand was why the teacher later complimented the boy who had asked that absurd question.
The boy had asked a question that had taken mathematicians several centuries to answer. Some mathematicians claimed that zero divided by zero was zero. Others claimed it to be unity. It was the Indian mathematician Bhaskara who proved that it is indeterminate.
The boy who asked the intriguing question was Srinivasa Ramanujan. Throughout his life, whether in his native Kumbakonam or Cambridge, he was always ahead of his mathematics teachers and is still ahead of most contemporary mathematicians.
- Anonymous (Found it while browsing)
- Anonymous (Found it while browsing)
Interesting! Thanks for sharing this.
ReplyDeletei think zero divided by zero is an indeterminate quantity not infinity...any number divided by zero gives infinity...but zero divided by zero is indeterminate...
ReplyDelete@Dhruva - I have just quoted the anecdote here. Not mine. Anyway, I will correct it here.
ReplyDelete