What is the basic idea/statement/puzzle etc.?

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The goal of this “paper” is to give you practice describing an interesting piece of mathematics to someone else in the class. This should be done briefly, so as to keep their attention, and passionately, so as to spark their interest. For the first goal, I’ll have you complete this assignment by answering some short-answer questions to give you a good format for brief communication. For the second goal, I suggest you find something you genuinely find interesting so that fascination comes through in your writing.
Some places to start (if you don’t already have something in mind):
https://www.youtube.com/user/numberphile/featured
https://www.youtube.com/channel/UCs4aHmggTfFrpkPcWSaBN9g
https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
List of theorems
https://blogs.scientificamerican.com/roots-of-unity/
https://www.maa.org/press/periodicals/maa-focus
The questions
Answer as if you’re explaining to a peer. Don’t forget your name and the title.
1. What is the basic idea/statement/puzzle etc.?
2. How does it work? Explain or briefly summarize the mathematics involved.
3. Why is it interesting, or, why do you find it interesting?

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