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### 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 dragon curve, which are easy to understand and explain, but are ...
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### '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 ...
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### How do I motivate myself to do math again? [closed]

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 ...
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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? ...
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Find $x$ in $$\Large 2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$$ A trick to solve this is to see that $$\large 2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}} \quad\implies\quad 2 = x^{\Big(x^{x^{x^... 9answers 1k views ### A Poster About Prime Numbers [closed] We're going to design a poster about prime numbers, which will appear in a mathematics magazine for middle school students. The poster should be both visually attractive and mathematically rich. Do ... 5answers 490 views ### Fractals reference I want to present an elementary lecture about Fractals in the Nature. So, I am searching open or online references with good pictures like the following one: I prepared a good program that makes ... 1answer 462 views ### Some questions about Fractals and software Ever since I read this article on math.SE I have been amazed by the wonder of fractals. I have been trying to learn what are fractals and how to write an equation for one, and I am truly confused, I ... 1answer 185 views ### Divisibility of the difference of powers Consider the following theorem: For any a, b \in \mathbb{Z}^+, there exist m, n \in \mathbb{Z} such that m > n and a\ |\ b^m - b^n. What's the best way to prove it? I have an idea (... 4answers 135 views ### Prove or Disprove the existence of a basis I'm asked to prove or disprove the existence of a basis (p_0,p_1,p_2,p_3) of F(t)(3) (Polynomials of degree at most 3) such that each of the polynomials p_0,p_1,p_2,p_3 satisfies the equation$$...
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 ...