## Mathematics of Love

###### By Anupum Pant

Online dating is a serious game these days. For any success of finding a mate online, Hannah Fry a lecturer in the mathematics of cities at the Centre for Advanced Spatial Analysis, has some really useful tips to share. Remember, all of these are backed by real math. Here is a quick rundown of the 3 most important points you should keep in mind if you are trying to find a partner online.

1. Be yourself. Turns out, trying to hide the ugly parts of yourself, you actually decrease your odds of receiving more messages. Counterintuitive, by completely backed by math.

2. According to optimal stopping theory, the math says that in the first 37% of your dating window, you should reject everybody for long-term relations. And when you are done with that, you should choose the next person that you think is better than everyone else you’ve dated before.

3. No compromise. Since 1 in two marriages fail, to avoid a marital breakup, it’s often mathematically
equivalent to see an argument between couples as an arms race. At least, the same equations are valid here too. Couples which spiral into a series of negativities are more prone to divorce than the couples who have bouts of positivity during arguments. So successful couples are the ones who do not let resentment built with time by having compromises. The ones who do not let anything unnoticed and allow each other to complain about everything.

## Gabriel’s Horn and the Painter’s Paradox

###### By Anupum Pant

If you take the plot of y=1/x and plot it from 1 to infinity, you’ll see that the plot seems to never meet the x axis. Now, take this plot and spin it fast with the x axis as the axis of rotation. You’ll then have a horn shaped solid object which is endlessly long. A mathematical object also known as the Gabriel;s horn or Torricelli’s trumpet.

Mathematically, this object is interesting because it can contain a finite amount of volume, but it’s surface area is infinite. That is to say, you can fill the horn/trumpet with a finite amount of paint, yet the whole paint it contains would not be enough to paint the inside surface of the object – known as the painter’s paradox. However, there’s a catch about painting the inner part of this horn. As WIkipedia puts it.

In fact, in a theoretical mathematical sense, a finite amount of paint can coat an infinite area, provided the thickness of the coat becomes vanishingly small “quickly enough” to compensate for the ever-expanding area, which in this case is forced to happen to an inner-surface coat as the horn narrows. However, to coat the outer surface of the horn with a constant thickness of paint, no matter how thin, would require an infinite amount of paint.

## Calculating Lego Combinations

###### By Anupum Pant

When Godtfred Kirk Christiansen was the third son of Ole Kirk Christiansen, the founder of LEGO went to the patent office to get a patent for lego blocks, he was asked a question by the patent officer to which he had no good answer. He only had an estimate. The question was – “How many combinations can 6 of the lego blocks be used to make different compound objects.”

He said he had calculated a number which was close to 102,981,000 combinations. He wasn’t quite right.
The question was so hard, that it took years to get to the exact answer. Soren Eilers, a professor of Mathematics at the University of Copenhagen put his mind to work and figured out the answer. In fact, his mind did not do him much service here. It was a computer which spit out the answer to him after a week long calculation.
He found that the actual answer to this mathematical conundrum is – 915,103,765

His computer can now calculate this number in a matter of minutes. But as you increase the number of blocks, the time needed to arrive at the answer increases hundred folds. So, the number of combinations from 7 blocks takes 2 hours. 8 blocks – around 20 days. But calculating the same for 9 blocks might take hundreds of years.