gif transformation from a flat torus to a horn torus to a spindle torus to a sphere and repeat

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Video with Transcript: Fibonacci Numbers hidden in the Mandelbrot Set - Numberphile

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0:00 So, today I'm gonna tell you about how the Fibonacci sequence appears in the Mandelbrot set. 0:04 Hopefully, your mind will be blown by the end of that sentence. 0:06 So the Fibonacci sequence, the rule is that you take the previous two numbers, 0:10 and you add them together to get the next. Right? So we started with 1 1. Their sum is 2. 0:15 The next number will be the sum of 1 & 2, which is 3. 0:19 The sum of 2 & 3 is 5. The sum of 3 & 5 is 8. I'll do one more. 0:24 And then, you can continue on. 0:26 Brady: "Easy." 0:27 Easy, right? And this occurs everywhere that has interesting connections to things in nature, and all of that, 0:31 but I just want to show you where it appears on the Mandelbrot set. 0:35 So, slightly less easy. So, the Mandelbrot set is a special object inside of the complex plane. So the plane of complex numbers. And 0:43 the way you cook this thing up is by 0:46 considering a certain type of dynamical system. So if you give me ...
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Video: The Mystery of 137 - Exploring a Most Illuminating Number

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Transcript Intro 0:01 hi everyone michael smith here 0:04 as a numerologist and former engineer 0:06 and stats guy i've always been 0:08 fascinated by number patterns especially 0:10 when the same pattern or number pops up 0:12 in many different places 0:14 one such number is 137 0:17 although it shows up in key places in 0:19 math physics chemistry and other natural 0:21 phenomena y has remained a mystery 0:24 in this video we're going to explore 0:26 this curious number from various angles 0:28 to see if we can shed some light on that 0:30 mystery Curious Appearances of 137 0:33 here are some of the better known 0:34 examples of where 137 shows up to give 0:37 you an idea of why it's considered so 0:39 intriguing 0:40 first and foremost the number 137 0:42 appears in one of the most important 0:44 universal constants of nature 0:46 what's called the fine structure 0:47 constant 0:48 with a value very close to 1 over 137 0:52 this number quantifies the strength of 0:54...
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Heisenberg's Uncertainty Principle Explained

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The video demonstrates Heisenberg's Uncertainty Principle through a laser experiment, explaining how narrowing a slit increases position precision but spreads momentum, showcasing light's wave-particle duality. Detailed Summary for [Heisenberg's Uncertainty Principle Explained]( https://www.youtube.com/watch?v=a8FTr2qMutA ) by [Monica]( https://monica.im )   [00:01](https://www.youtube.com/watch?v=a8FTr2qMutA&t=1.56) This video demonstrates Heisenberg's Uncertainty Principle through a laser experiment, illustrating how narrowing a slit affects the behavior of the light spot on the screen.   - Introduction to the experiment showcasing Heisenberg's Uncertainty Principle.} - Observation of the laser spot's behavior as the slit is narrowed.} - Unexpected result: the spot on the wall widens as the slit narrows.} - Introduction to Heisenberg's Uncertainty Principle and its implications on position and momentum.}        [01:26](https://www.youtube.com/watch?v=...
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