Squaring the Circle

More than a century ago, Rabindranath Tagore wrote the lines:

E kebol diney raatre jol dhele futa paatre
Britha cheshta trishna mitabaare.

(It is like pouring water all day into a leaky pitcher,
Trying in vain to quench your thirst.)

He was writing about complex things like human desire for wealth, but the things that reminded me of those lines after all these years are quite simple: a square and a circle.

I have a photograph that would have made things clear in an instant, but since I am a little doubtful about the legality of publishing that photograph here, I have to take the long drawn route of using a thousand words instead.

To make a long story short, I had to grade a bunch of Java exam papers on Friday. My students are all science or engineering undergraduates and so, when we set a question asking them to write a function to calculate the area of a square given its side and the area of a circle given its radius, we did not think it was necessary to supply the formulae for them.

Big mistake. It turns out that at least 30% of the class did not know those formulae and got them wrong.

I must give them credit where it's due though; everyone knew that finding the area of a circle involves some sort of calculation involving a pi. Some even knew the value of pi. But that was about the extent of their knowledge. In the few hours of grading, I discovered that the area of a circle could be any one of the following, apart from the usual pi*radius*radius:

• 2*pi*radius
• pi*pi*radius
• 2*pi*radius*radius
• 4*pi*radius*radius
• pi*pi*radius*radius
• 2*pi*pi*radius*radius

I may have forgotten a few, but that should give you the general idea.

People seemed much more knowledgeable on the subject of squares. Most of them wrote it correctly as side*side. However, some of the more interesting answers were:

• 2*side
• 4*side
• 2*side*side
• length*height (these two parameters were not defined in the problem)
• side*side*side*side

By the evening I had all but forgotten the real things. I deducted one mark per formula error. My colleague who is also a TA felt I was being too harsh on the students. After the papers were returned in class, I did have to answer a few questions. Some of them were from the girl with the side*side*side*side. She tried to support her answer by this line of argument:

• She was just a freshman (a college first year) and didn't know all those complex formulae yet.
• This was a computer science exam and the mathematical formulae should have been provided.
• Nobody remembers all that stuff nowadays anyway.
• Rest of her program was correct.
• A square has four sides.

Finally I had to tell her that it would be unfair to the students who got it right if I gave her full marks, and that made her leave. She seemed far from convinced though. After all a square does have four sides. Thankfully, she did not try to prove side*side = side*side*side*side using a square with side 1 as example. I have faced that sort of thing before and it is NOT funny.

I hope you see now what made me remember Tagore's lines and what that initial rant about pouring water into leaky pitchers was all about.