I want to know: what is the last digit of $\pi$? Some people say there are no such thing, but they fail to mention why.

So I got that there is two cases: odd or even. If odd then say $n^2$ is $(2k+1)^2 = 4k^2 + 4k + 1.$ then $4k^2 + 4k + 1 + 5$ would need to be divisible by...

I am working on a UAV project that requires calculating the ground sampling distance (GSD) in order to retrieve the meter/pixel scale. The GSD for nadir v...

Let $P\to M$ be a $\mathrm{SU}(2)$-principal bundle over a closed connected manifold $M$. Let $A$ be a flat connection on $P$, fix $x\in M$ and let $H:=\m...

I have an algebra final exam on tuesday, and I'm having some trouble with this kind of exercise. I tried looking for an explanation in all over the w...

My lecture notes say: A polynomial on $\mathbb{R}$ is a function $f: \mathbb{R} \to \mathbb{R}$ with $x \mapsto \sum_{k=0}^n a_k x^k$ with $n \in \mathbb{...

How do I go about factoring this problem? What is the best method? I can not factor out an $x$ since the $12$ does not have a variable. I usually use the ...

How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?

Given a point $Q$ and $2d$ Cubic Bezier Curve: $$P = A(1-t)^3 + 3Bt(1-t)^2 + 3Ct^2(1-t) + Dt^3$$ Is there a way to know which side of the curve the point ...

I knew how to do this long ago, found the exact problem in my old trig book, but I can't seem to work it out. Say I'm at an unknown distance fro...