Linked Questions

580
votes
48answers
380k views

Visually stunning math concepts which are easy to explain [closed]

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 dragon curve, which are easy to understand and explain, but are ...
180
votes
64answers
41k views

'Obvious' theorems that are actually false

It's one of my real analysis professor's favourite sayings that "being obvious does not imply that it's true". Now, I know a fair few examples of things that are obviously true and that can be proved ...
46
votes
15answers
5k views

How do I motivate myself to do math again?

I have been thinking of asking for help for a few months now but posting in a public forum like this is intimidating. Still, I am currently in a university studying mathematics as an undergrad. I took ...
26
votes
20answers
2k views

Interesting Math for 3-graders

I'm supposed to give a 30 minutes math lecture tomorrow at my 3-grade daughter's class. Can you give me some ideas of mathemathical puzzles, riddles, facts etc. that would interest kids at this age? ...
59
votes
4answers
4k views

Are the solutions of $x^{x^{x^{x^{\cdot^{{\cdot}^{\cdot}}}}}}=2$ correct?

Problem: Find $x$ in $$\large x^{x^{x^{x^{ \cdot^{{\cdot}^{\cdot}} }}}}=2$$ Trick: $x^{x^{x^{x^{\cdot^{{\cdot}^{\cdot}}}}}}=2$, so, $x^{(x^{x^{x^{\cdot^{{\cdot}^{\cdot}}}}})}=x^2=2$, and, ...
10
votes
9answers
1k views

A Poster About Prime Numbers [closed]

We're going to design a poster about prime numbers, which will appear in a mathematics magazine for middle school students. The poster should be both visually attractive and mathematically rich. Do ...
22
votes
5answers
385 views

Fractals reference

I want to present an elementary lecture about Fractals in the Nature. So, I am searching open or online references with good pictures like the following one: I prepared a good program that makes ...
2
votes
1answer
339 views

Some questions about Fractals and software

Ever since I read this article on math.SE I have been amazed by the wonder of fractals. I have been trying to learn what are fractals and how to write an equation for one, and I am truly confused, I ...
0
votes
1answer
162 views

Divisibility of the difference of powers

Consider the following theorem: For any $a, b \in \mathbb{Z}^+$, there exist $m, n \in \mathbb{Z}$ such that $m > n$ and $a\ |\ b^m - b^n$. What's the best way to prove it? I have an idea ...
1
vote
4answers
110 views

Prove or Disprove the existence of a basis

I'm asked to prove or disprove the existence of a basis $(p_0,p_1,p_2,p_3)$ of $F(t)(3)$ (Polynomials of degree at most 3) such that each of the polynomials $p_0,p_1,p_2,p_3$ satisfies the equation ...
2
votes
1answer
40 views

Variance of event counting

I have this question (not homework, review problem for qualifying exam), tried approaching it a couple of ways (unsuccessfully). Any recommendations? Let $X_1,..,X_n$ be i.i.d continuous rvs. A ...