Skip to main content

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.


Comments

Post a Comment

Popular Posts

1940 - Siege of Calais

(Audio enhances reading experience) 21 May 1940 “My good men, I come to you with grave news. The beaches of Calais will continue to be lonely tomorrow. There will be no boats at dawn.  Word has come from London and it seems lads, ‘home’, has just been turned to a mere word of nostalgia and not something we can hope to see, ever again.  The fat politicians sitting in parliament have sent their gravest apologies and perhaps think that we have surrendered to the Germans already. The Prime Minister has personally put in his apology through the wire too, cursing our enemy to his full capacity.  I did not bother noting down all that. Because I don’t for one moment believe in surrender, or defeat. Yes, even defeat. We men of war may lose our lives in the coming hours but with God himself as our witness I can assure you good lads.. A soldier never dies in vain nor defeat!  ‘Home’, has just been turned to a mere word of nostalgia and not something we can hope to s...

Empathy's Demise

It's quite wonderous really, How clocks around the world are ticking right now in perfect synchrony. Wonderous how even in such a large world,  We are all nakedly defined by a common present.  A common, now. Wonderous how the sun is setting right this moment, In one corner of the world. While it rises in another, all at the same time. . Perhaps it is all that's left that unites us through the present. Only the sun bears witness to the capering of man,  For the world is simply too large for us. Large enough to let a man in Paris grab an afternoon Latté,  While a woman in Casablanca runs to the sweet embrace of her lover. . Large enough that the loudest sound you hear is this poem, and my voice, Sheltered from the shelling beyond the seven seas. Large enough that at this very second, There's a little girl with ringing ears, Looking through the rubble, For her dead mother. . Now, when my voice too goes quiet.  I implore you, tell me what is louder. Is it the luxury...

Novelty of the Mind

Every thought one can have is nothing but a complex and new permutation of known facts and memories. A man without any memory, knowledge or experience of all life senses technically, should not be able to imagine, well... anything! Every thought we have is but a mere extrapolation and combination of pre existing thoughts. Or is it something more.  Our thoughts are but a product of all stimuli ever received. Just piled up. Being consumed, processed, replayed, remodelled.. In all the permutations and combinations that strike our mind first. I would honestly love to be disproven in this matter. It is eerie how missed out experiences in life contribute more to our path than we could ever know. Merely because, we do not know what we've missed out on! Stimuli is replayed behind our eyes again so that we make sense of the world around us. The catch is, this constantly changes the way we think or - the permutations used before the memories fade. Forcing us through a fixed, rigid path of wa...