Senior's Dream

In which I finally prove an elusive identity. #WakandaForever

The Jacobian & Divergence

In which I try to change variables in multiple integrals using divergence theorem. I sort of succeed.

The Jacobian & Determinants

I look into the source of using the Jacobian when we change variables.

Basel's Problem - New proof and some calculus

Sorry for the long hold up on another post. This new post is a result on my investigations on a proof of \(\zeta(2) = \frac{\pi^2}{6}\) by Daniele Ritelli. Yes, it's another post on something Euler solved first. But I did things different this time around: I discussed …

Area and Perimeter of Astroids

It is about time I revisited my first adventure Envelopes and Astroids. In the end of the post, I named the envelope of the line segments an Astroid. I will now find two basic properties of this shape: area and perimeter.

Envelopes and Astroids

Envelopes kept cropping up in my doodles but I never gave them much attention. Up until the day I started drawing line segments of a constant length, say \(1\), from one side of a piece of paper to an adjacent side (See Fig 1). It appeared that these lines were …