Articles of popular math

What is the best strategy for Cookie-Clicker-esque games?

Today, I stumbled across the game Cookie Clicker, which I recommend you avoid until you have at least a few hours of time to waste. The basic idea behind the game is this: You have a large stash of currency, which constantly increases at the given rate. At any given time, you have a series […]

Explaining what real math is to a high school student

I think, after reading through some of the questions here and their answers, that there are many people here who share my opinion on high school mathematics that it’s quite different from “real mathematics” as taught at university. I’m not only talking about the difficulty, but much more about the way it is taught and […]

Sheldon Cooper Primes

On the $73^{\text{rd}}$ episode of the Big Bang Theory, Dr. Sheldon Cooper, an astrophysicist portrayed by Jim Parsons $(1973 – \stackrel{\text{hopefully}}{2073})$ revealed his favorite number to be the sexy prime $73$ Sheldon : “The best number is $73$. Why? $73$ is the $21^{\text{st}}$ prime number. Its mirror, $37$, is the $12^{\text{th}}$ and its mirror, $21$, […]

Prove that $\pi>3$ using geometry

I was asked this question today in an interview. Question: Prove that $\pi>3$ using geometry. They gave me hints about drawing a unit circle and then inscribing an equilateral triangle and then proceeding. But I could not follow. Can anyone help?

The Monty Hall problem

I was watching the movie 21 yesterday, and in the first 15 minutes or so the main character is in a classroom, being asked a “trick” question (in the sense that the teacher believes that he’ll get the wrong answer) which revolves around theoretical probability. The question goes a little something like this (I’m paraphrasing, […]

What is the solution to Nash's problem presented in “A Beautiful Mind”?

I was watching the said movie the other night, and I started thinking about the equation posed by Nash in the movie. More specifically, the one he said would take some students a lifetime to solve (obviously, an exaggeration). Nonetheless, one can’t say it’s a simple problem. Anyway, here it is $$V = \{F:\mathbb{R^3}/X\rightarrow \mathbb{R^3} […]

A golden ratio series from a comic book

The eighth installment of the Filipino comic series Kikomachine Komix features a peculiar series for the golden ratio in its cover: That is, $$\phi=\frac{13}{8}+\sum_{n=0}^\infty \frac{(-1)^{n+1}(2n+1)!}{(n+2)!n!4^{2n+3}}$$ How might this be proven?

Mathematics understood through poems?

Along with Diophantus mathematics has been represented in form of poems often times. Bhaskara II composes in Lilavati: Whilst making love a necklace broke. A row of pearls mislaid. One sixth fell to the floor. One fifth upon the bed. The young woman saved one third of them. One tenth were caught by her lover. […]

“What if” math joke: the derivative of $\ln(x)^e$

Randall Munroe, the creator of xkcd in his latest book What if writes (p. 175) that the mathematical analog of the phrase “knock me over with a feather” is seeing the expression $ \ln( x )^{e}$. And he writes regarding this expression: “it’s not that, taken literally, it doesn’t make sense – it’s that you […]

How Can One Prove $\cos(\pi/7) + \cos(3 \pi/7) + \cos(5 \pi/7) = 1/2$

This question already has an answer here: $\sum \cos$ when angles are in arithmetic progression [duplicate] 1 answer