## Region between Polar Curves

Every once in a while you'll get a piece of maths which will elicit a response of "wat?" Find the area of the region inside the rose $ r=4\sin2\theta $ and inside the circle…

Every once in a while you'll get a piece of maths which will elicit a response of "wat?" Find the area of the region inside the rose $ r=4\sin2\theta $ and inside the circle…

Simpson's rule is given (in my textbook) as such: $$ \int_{a}^{b}f(x)\approx \text{S}(n),2|n $$ $$ \text{S}(n)=\left[ \begin{matrix} f(x_0) + 4f(x_1) + 2f(x_2…

A little under a half a year ago a Legend among us switched careers. (Pun very much intended). I'm normally a quiet type that doesn't weigh-in on topics like this often, but some of the…

We've all heard the complaints before: "I just don't get maths!" "Oh no, not a maths problem! I failed that in school!" There is a pervasive fear and resentment of mathematics in westernized society, bordering…

I recently had to set up an internal wiki for my workplace. I picked MoinMoin because it wasn't written in PHP and therefore I believe it will present fewer security risks to my production server…

This is a really cool trick I only recently learned. Evaluating limits has useful applications, and this little trick allows the evaluation of limits which, on the surface, seem impossible. Consider $$ \lim_{x\to 0…

Let $i=\sqrt{-1}$, and let $e^{x}=\sum_{k=0}^{\infty}\frac{x^{k}}{k!}$.1 If follows that $$ e^{ix}=\sum_{k=0}^{\infty}\frac{\left(ix\right)^{k}}{k!}. $$ Utilizing series expansion…