This is by far my favourite mathematical proof. Below are 2 ways of doing it. eulers-formulaDownload

I was recently helping a friend with his coursework on vectors when I decided that it would be an interesting challenge to derive what we use as the "dot" and "cross" products and why we bother having these around in the first place. Beyond just lines and planes in space, these have interesting applications in … Continue reading Dot and cross product →

I saw this question posted on a board at my old high school. Apparently, it was a problem asked at an Oxford interview. It read, "Prove that centripetal acceleration is the square of the velocity over the radius of the circle". Try to solve it, and see here for my solution.

This is a question that crossed my mind when conducting a mock interview for a prospective Engineering candidate. The capacitor and inductor have time-dependent charging and discharging curves that you might have familiarised yourself with in high school.  While these curves are intuitive, how do we mathematically derive their equations? How do we relate charge, … Continue reading Capacitors and inductors →