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### What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) [closed]

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's Lament,...
26k views

### Visually deceptive “proofs” which are mathematically wrong

Related: Visually stunning math concepts which are easy to explain Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually ...
20k views

### Easy math proofs or visual examples to make high school students enthusiastic about math [closed]

I'm a teacher in mathematics at a high school. Math has fascinated me for almost my entire life, so I would like to bring that enthusiasm to my students with beautiful yet easy to understand proofs or ...
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### Intuitive understanding of the derivatives of $\sin x$ and $\cos x$

One of the first things ever taught in a differential calculus class: The derivative of $\sin x$ is $\cos x$. The derivative of $\cos x$ is $-\sin x$. This leads to a rather neat (and convenient?) ...
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### Irrational numbers in reality

I have a square tile which measures 1 metre by 1 metre, by the Pythagorean identity the diagonal from one corner to another will be $\sqrt 2$ metres. However $\sqrt 2$ is an irrational number, could ...
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### What is the explanation for this visual proof of the sum of squares?

Supposedly the following proves the sum of the first-$n$-squares formula given the sum of the first $n$ numbers formula, but I don't understand it.
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### What exactly are fractals

I have always been amazed by things like the Mandelbrot set. I share the view of most that it and the Koch snowflake are absolutely beautiful. I decided to get a deeper more mathematical knowledge of ...
529 views

### Proving $x^2+x+1\gt0$

I was doing a question recently, and it came down to proving that $x^2+x+1\gt0$. There are of course many different methods for proving it, and I want to ask the people here for as many ways as you ...
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### Pythagorean Theorem Proof Without Words 6

Your punishment for awarding me a "Nice Question" badge for my last question is that I'm going to post another one from Proofs without Words. How does the attached figure prove the Pythagorean ...
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### Textbooks for visual learners

Perhaps this question has already been asked (if so, please let me know) but I am looking for books that appeal to visual learners. I discovered that I am able to understand concepts much quicker ...
62k views

### Why $\cos(-\theta)$ gives positive values while in case of sine it is negative?

Why $\cos(-\theta)$ gives positive values while in case of sine it is negative? I mean $\cos(-\theta) = +\cos(\theta)$ $\sin(-\theta) = -\sin(\theta)$ $\tan(-\theta) = -\tan(\theta)$ and please ...
802 views

### What areas of math can be tackled by artificial intelligence?

Artificial intelligence is nearing, with image/speech recognition, chess/go engines etc. My question is, what areas of math that are interesting to mathematicians, is likely to be the first to be able ...
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### Why do some series converge and others diverge?

Why do some series converge and others diverge; what is the intuition behind this? For example, why does the harmonic series diverge, but the series concerning the Basel Problem converges? To ...