I was trying to make some triangles when $2$ sides and the non-included angle was given. When the angle given was below $90$ degrees, there were two possi...

I've been looking into the Toeplitz' Conjecture and became very interested, so I began to study it. Here is the conjecture: For any Jordan curve...

Good morning/evening to everybody. I'm interested in proving this proposition from the Green's first identity, which reads that, for any suffici...

I will demonstrate why the group of rotational symmetries of a Dodecahedron is $A_5$. For that, we have to find five nice objects, on which the group of s...

Doing a normal Taylor expansion of $\arccos(1-x)$ around $x=0$ to two terms by taking derivatives doesn't work because of division by zero. I've...

Let $X$ be a topological space and $N$ a subset of $X$. I want to show that $\partial \bar N\subset \partial N$. I know that since $\bar N$ is closed then...

I am studying Fourier analysis on my own, I realised that probably the first thing you want to proof in Fourier transform is that the sum of 2 sinuoids (n...

This is the image: So the question is: (a) Ralph is painting the barn, including the sides and roof. He wants to know how much paint to purchase. What is ...

So I understand that a quartile is a quantile where the data is divided into four groups. 1 2 3 ---|---|---|--- And 1, 2, and 3 are the quartiles. The sec...

How would you determine whether to use dx or dy? I uploaded a scenario where we revolve around x=6 but we must use dx for the shell method.