Here's the Geometric Series proof more rigorously, before someone accuses me of being a physicist — waitpic.twitter.com/R8KTw4rcSS
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I went full @3blue1brown and used Manim to illustrate the proof of the Geometric Series formulapic.twitter.com/c3kVy63SIh
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Here's my python source code for the animation. The library manimlib is
@3blue1brown's graphics engine.https://github.com/InertialObservr/manim_projects/blob/master/geometric_series.py …Show this thread
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Ayyyyy, I've been learning Manim too! Here's a clip of the animations used in a presentation explaining markov chains:pic.twitter.com/4pgXnjOUKW
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Nice! yea it really is a wonderful little graphics engine .. pretty intuitive too
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Feedback: you need to leave a ghost of the previous formula, otherwise you can't see what's happened. So, just duplicate the object before moving and animating it.
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thanks for the feedback! i considered that at first but it was quickly becoming cluttered, though you're right i could have at least left the main formula up
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Looks great... buuuuut...sorry to be "that guy"... technically you're starting from the assumption that the series converges at all, which you do not prove with this. Similar to the "1+2+3+4+...= -1/12" argument, right?
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Suppose S is finite in step 1 & there we have it the difference between this heuristic and the -1/12 one is that 1-1+1.. diverges always This converges for |r|<=1, and so while nits can be picked, at the end of the day I didn’t want to code up the condition
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But no 3b1b voice so YOUR PROOF IS BAD >:(
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i already put enough time into this .. it really gives you an appreciation for the time he must invest into those videos
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