Vedang Mahajan

There was a young fellow from Trinity Who took square root of infinity Square root of But the number of digits Gave him the fidgets; He dropped Math and took up Divinity. -- George Gamow (One Two Three...Infinity)  So what really is infinity? Infinity is an idea. It isn't really a concrete number. It is something that never ends, it goes on forever.  Transfinite Numbers As kids, all of us have baffled over the idea of the largest number there is. That’s when we came across “infinity” and we were told that it is the biggest “number”. Nevertheless, our curiosity wouldn't settle. Is there anything beyond that? If so, what is it? What if it told you there is. Well... sort of. Some infinities are bigger than others.  This idea can help you say that there are more points on a 1cm line than there are rational numbers in the universe or that there are an equal number of even numbers and even and odd numbers combined.  There is an infinite number of natural numbers (1,2,3 and...

Picture yourself as a cop. You are in your jeep (which is stationary) on a patch of sand which happens to be one one of the sides of a cement road. On the other side of the cement road, there is an identical patch of sand on which there is a notorious criminal in his vehicle. You have been assigned to capture the criminal and bring him to justice.      To chase him, you need to approach him in your vehicle, but there is a catch. As soon as you start, the criminal will hear the sound of your engine. As of now, he/she doesn’t know where you are but the hum of your engine will give yourself away. You need to find the fastest path to the culprit and remember your jeep is much faster on the road than it is on the dust track. The question here is, — what will the fastest path look like? The answer may surprise you at first. The fastest way to get to the criminal will be by meeting the road at a 42 degree angle. This is because of  Fermat’s Principle . Here we introdu...