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Showing posts from October 27, 2022

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