general
Definition of a metric
I'm having a hard time understanding what the definition of a metric is. From what I think I understand, it's just a method of measurement betwe...
Apr 14, 2026
Archive: General
general
A triangle inscribed in a circle of radius $2$ has angles $45^\circ$ and $60^\circ$. What's its area?
Points $A$, $B$ and $C$ are on the circumference of a circle with radius 2 such that $\angle BAC = 45$ and $\angle ACB = 60$ . Find the area of $\triangle...
Apr 14, 2026
general
Why $\tan x>\sin x$ in this question?
The question asks me to prove the identity $\tan ^2x-\sin ^2x=\tan^2 x \sin^2 x$ and use this result to explain why $\tan x>\sin x$ for $0<x<90$ ...
Apr 14, 2026
![Sum the series : $\frac{1}{9\sqrt11 + 11\sqrt9} +\frac{1}{11\sqrt13 + 13\sqrt11} +\ldots$ [closed]](https://news.conceivablytech.com/uploads/sum-the-series-frac-1-9-sqrt11-11-sqrt9-frac-1-11-sqrt13-13-sqrt11-ldots-closed_720.jpg)
general
Sum the series : $\frac{1}{9\sqrt11 + 11\sqrt9} +\frac{1}{11\sqrt13 + 13\sqrt11} +\ldots$ [closed]
$$\frac{1}{9\sqrt11 + 11\sqrt9} + \frac{1}{11\sqrt13 + 13\sqrt11} + \frac{1}{13\sqrt15 + 15\sqrt13} + \ldots + \frac{1}{n\sqrt{n+2} + (n+2)\sqrt{n}} = \fr...
Apr 14, 2026
general
Looking for the name of block diagonal decomposition
I remember there exist a decomposition such that it transforms any given matrix to a block diagonal matrix, and each block having single eigenvalue. I cou...
Apr 14, 2026
general
Visually stunning math concepts which are easy to explain
Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the drag...
Apr 14, 2026
general
2+2=4; Not in the Z3 algebraic group
I was reading the article/wiki here When I came across this quote ObviousFact?: examples: 2+2=4 for most people Those with higher mathematical knowledge m...
Apr 14, 2026
general
what's the derivative of $\cos(x) \sin(x)$
before I ask for anything I must admit I'm working hard to understand this beautiful subject. Thanks in advance. I want to get a derivative of: $\cos...
Apr 14, 2026
general
The Sum of 5 Consecutive Integers is 505, what is the Third number in this Sequence?
So I've never covered this and I'm a bit confused. $$x + (x+1) + (x+2) + (x+3) + (x+4)$$ So $5x + 10 = 505$ which equals $x = 99$. So isn't...
Apr 14, 2026
general
Difference between $\{a\}$ and $\{\{a\}\}$ in Sets
I am presently a 11th grader. I came across a question which was to answered of True or False in the Sets chapter. Let me just text down the complete ques...
Apr 14, 2026
