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The Beauty of Dandelin Spheres


I've been fortunate enough to run into this seemingly tame video about ellipses by 3Blue1Brown, and I think I've found a nice anchor to base my love for math on. Though I read about it in textbooks and was content enough to feel I understood it, I never stopped to ponder why an angled section of a cone would give an ellipse. And I mean going down into the depths of it to really find a mathematically sound way I could represent it.

I think this provides a good insight into how our imaginative minds work too. I often find myself feeling convinced of something when I successfully understand the bare basics of it. Maybe this has something to do with the Dunning Kruger effect? Perhaps so. Maybe our minds are still primitive in this sense. Even a plastic shovel can do the job of lifting off the topsoil and so can an excavator. But to dig deep into the earth, a shovel breaks immediately. And so do weak superficial proofs which provide immediate satisfaction. 

I couldn't have been bothered to delve deeper into how that actually worked than be convinced seeing a cone being sliced in my head. It's funny how almost all banes of our mental reward system come from the fact that our brains are still hardwired to caveman parameters! Procrastination, Gluttony, and the arch enemy of curiosity. Never mind, all this for another day maybe.

Seeing how Dandelin 🠉 proves this using clever geometry has put a broad smile on my face. This is probably one of my favourite mathematical proofs, not because of its potential to be expressed visually alone, but also because of how simple and fundamental the pre requisites to understanding it are. I highly recommend watching the video yourself.


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