Why is pi here? And why is it squared? A geometric answer to the Basel problem
A most beautiful proof of the Basel problem, using light. More problem-driven learning: https://brilliant.org/3b1b Content like this is made possible by the very ...
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I'm gonna guess that you have never had the experience of your heart rate increasing in excitement while you are imagining an infinitely large lake with lighthouses around it Well if you feel anything like I do about math, that is gonna change by the end of this video Take 1 plus 1/4 plus 1/9 plus 1/16... (and so on) where you're adding the inverses of the next square number. What does this sum approach as you keep adding on more and more terms? Now this is a challenge that remained unsolved for ninety years after it was initially posed, until finally it was Euler who found the answer, super surprisingly, to be pi squared divided by 6. I mean isn't that crazy, what is pi doing here and why is it squared? We don't usually see it squared. In honor of Euler, whose hometo...
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I'm gonna guess that you have never had the experience of your heart rate increasing in excitement while you are imagining an infinitely large lake with lighthouses around it Well if you feel anything like I do about math, that is gonna change by the end of this video Take 1 plus 1/4 plus 1/9 plus 1/16... (and so on) where you're adding the inverses of the next square number. What does this sum approach as you keep adding on more and more terms? Now this is a challenge that remained unsolved for ninety years after it was initially posed, until finally it was Euler who found the answer, super surprisingly, to be pi squared divided by 6. I mean isn't that crazy, what is pi doing here and why is it squared? We don't usually see it squared. In honor of Euler, whose hometo...
