When a mathematician gets bored

Though I'm sure these results are somewhat well known, (in fact I firmly believe Euler derived these fascinating identities as some side quest) it is, nonetheless, a lovely little exercise showcasing how boredom can lead to productivity. My complex analysis lectures:    • Complex Analysis Lectures   Support my work and get early access to content via Patreon:   / maths505   You can follow me on Instagram for write ups that come in handy for my videos and DM me in case you need math help: https://instagram.com/maths.505?igshi... My LinkedIn:   / kamaal-mirza-86b380252   Advanced MathWear: https://my-store-ef6c0f.creator-sprin...