A comprehensive list of binomial identities?
Is there a comprehensive resource listing binomial identities? I am more interested in combinatorial proofs of such identities, but even a list without pr...
Apr 15, 2026 1 VIEWS
Topic: General
5104 Articles 
Circle rotating within a circle (roulette)
This was something in a course of mine I'm a bit too thick to see. If one takes a circle of radius $3$ and a circle of radius $1$, and rolls the smal...
Apr 15, 2026 1 VIEWS
How can I flip the signs of this denominator without affecting the rest of the equation?
I am trying to solve an equation for x and I seem to be making a mistake in how I multiply by -1. First I simplified the equation to: $$\frac{(x-1)(x-1)}{...
Apr 15, 2026 1 VIEWS
What is the importance of knowing if a series converges or diverges? [closed]
This semester I have been given a multitude of techniques for discovering if a series converges or diverges with no explanation for why I would need to kn...
Apr 15, 2026 1 VIEWS
How many ways to write a number $n$ as the product of natural numbers $\geq 2$?
I am looking for a closed form (or efficient algorithm) for $f(n)$, the number of ways in which $n$ can be written as a product of natural numbers $\geq 2...
Apr 15, 2026 1 VIEWS
Help with alpha-cuts in fuzzy sets
basically all I need to know is what are the standard methods to achieve the below. So, I have a fuzzy set A containing (say) four elements. For each elem...
Apr 15, 2026 1 VIEWS
Finding shortest distance between a point and a surface
Consider the surface $S$ (in $\mathbb R^3$) given by the equation $z=f(x,y)=\frac32(x^2+y^2)$. How can I find the shortest distance from a point $p=(a,b,c...
Apr 15, 2026 1 VIEWS
Examples of convex sets
A set $K \subset \mathbb{R}^n$ is called convex if for each $x,y \in K$ and for each $0 \leq \lambda \leq 1$, $(1- \lambda)x+ \lambda y \in K$. $$D=\{ (x_...
Apr 15, 2026 2 VIEWS
Questions tagged [infinity]
Q&A for people studying math at any level and professionals in related fields
Apr 15, 2026 1 VIEWS
Can a perfect square be only an integer number?
Can a perfect square only be an integer number? Can this idea be extended to real numbers or rational numbers?
Apr 15, 2026 2 VIEWS
Does loga/logb = log(a^(1/logb))?
I know $\log(a^b)=b\log(a)$. However, Wolfram Alpha tells me that $\frac{\log(a)}{\log(b)}$ does not equal $\log(a^\frac{1}{\log(b)})$. Is Wolfram Alpha c...
Apr 15, 2026 1 VIEWS
Trigonometric Identify: $(1+\cos{x})/\sin{x}=\cot{(x/2)}$
I am having trouble with this. I have tried many times already. I just can not figure out how to deal with the $x/2$. $$\frac{1+\cos{x}}{\sin{x}}=\cot{\fr...
Apr 15, 2026 2 VIEWS