I was on the internet, where I found the equation $[(1/2)!]^2 \cdot 4 = \pi$, so like any curious person, I used a calculator to see whether or not it was...

Use sketch to find exact value of $\tan (\cos^{-1}\dfrac{5}{13})$ I drew a right triangle with angle $\theta$ and sides $12,5,3.$ If $\cos \theta=\frac{5}...

I'm trying to determine the volume of the solid that is obtained by rotating around the $x$-axis the region limited by $y=2x$ and $y=x^2$. I'm t...

I have two points in the 2D space, e.g. point A is (3, 2) and point B is (30, 20) I want to get some points in between, aka, interpolating between A and B...

I've taken multivariate calculus and am wondering if I can see a specific function where the order of taking the partial derivative matters. I'v...

I was playing mental maths in which we solve problems without pen and pencil. Then I came across a problem $$\sqrt {6 \sqrt{6 \sqrt{6\sqrt\cdots}}}.$$ I a...

Let $ p $ be a prime number and $ A \subset \mathbb{Z}/p\mathbb{Z} $. Suppose $ 0 \notin A $ and for $ a \in A $ define $ d(a)= \min\{k|-a \in \underbrace...

When is a proof or definition formal? I've been searching for an explanation of when or proof or definition is formal. Sometimes, authors call their ...

Q&A for people studying math at any level and professionals in related fields

A simple question. They give the definition of permutation as "a one to one mapping of the set onto the set of positive integers $\{1, 2,3,4, \ldots n\}$....