How a geometry problem turned into a simple social experiment.

Question for the day: Find area of the shaded region

One of my friends posted this picture in a WhatsApp group, and it made me traverse all the path back to my school days. I had little imagination that this picture would awaken a few fundamental questions about the way we learn, process and perceive such questions in daily life. I reposted this picture in multiple groups, and ran a small social experiment; it was interesting to see the responses.

I classified the responses and made 3 segments for the responders.

Non-believers were the ones who have seen such things in life, but purely chose to ignore because of a multitude of reasons; maybe the fact that they hated math in school or for the fact that they were quite tired to pursue an old geometry problem late at night. Believers are the ones who liked a challenge thrown at them and partially or completely solved the problem. I was more interested in the outlier responses. “Why are we even solving these problems?, haven’t we suffered an ordeal going through such problems in yesteryears?”. “Are you jobless and studying for CAT again?”

After spending an hour on a not-so-easy problem, the shaded area was found, but it’s the questions asked by my friends which motivated me to write on it. I wanted to understand my own motivation for trying to solve this problem in the first place. In that 1 hour, I experienced disappointment, resilience and pure elation solving the problem after a few attempts (I think I am a sucker for math and physics problems). The process is what I enjoyed, rather than the final answer. The pure neural firing of old, associated connections to finally derive the answer, was nothing short of an ecstasy when my brain’s reward center decided to release the required hormones.

Sometimes, it is important to understand the process we go through, and deeply introspect on it. I think my friends either didn’t know how to do such problems or never liked doing such problems. I believe it is the 2nd reason, because the sample set I used were engineers, math & science students, so they are aware of trigonometry and geometry concepts.

Was it the way that we were taught, the reason to the ‘outlier’ responses? Did we build up a generation which is quite clueless about how to achieve their potential? Our educational institutions are primarily based on a ‘teach to test’ concept. Our schools never answered the questions of ‘why’ we are doing something. More importantly, many of us failed the answer of ‘why’ we are doing ‘what’ we are doing. These are the same set of problems we practised day-in and day-out to crack the exams required to reach where we are today. Retrospectively, many didn’t like these problems. The question to be answered is, if there was no genuine interest for such problems to reach where we are today, do you think solving the problems thrown at us today, is what we actually want to solve?

On a lighter note, this is the solution, of course there should be an easier way to solve it. Enjoy!