An unsolved conjecture, and a clever topological solution to a weaker version of the question.
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Home page: www.3blue1brown.com/
— 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if youre into that).
Смог нарезать с помощью фрезы ( ali.pub/5dps3b ) на токарном станке многозаходную ( десять заходов ) резьбу в два направления, сразу и правая и левая на одном болте.
Музыка от Epidemic Sound (http://www.epidemicsound.com): https: www.epidemicsound.com/referral/13czek/
An exploration of infinite sums, from convergent to divergent, including a brief introduction to the 2-adic metric, all themed on that cycle between discovery and invention in math.
Home page: www.3blue1brown.com/
Music: Legions (Reverie) by Zoe Keating
— 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if youre into that).
If you are new to this channel and want to see more, a good place to start is this playlist: goo.gl/WmnCQZ
— 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if youre into that).
If you are new to this channel and want to see more, a good place to start is this playlist: 3b1b.co/recommended
Если Вы хотите её попробовать, я должен предупредить Вас, что это не самый задокументированный инструмент со своими причудами, которые можно было бы ожидать от библиотеки, которую кто-то написал только для себя.
Музыка в начале:
Candlepower от Chris Zabriskie лицензирована под Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
Источник: chriszabriskie.com/divider/
Музыкант: chriszabriskie.com/
Если вы хотите помочь с переводом субтитров или проверкой перевода, уже сделанного другими и ожидающего одобрения, нажмите на шестерёнку в видео, перейдите в «Субтитры», потом «Добавить субтитры». Я очень ценю тех, кто помогает с этим, так как это делает мои видео доступными многим людям.
— 3blue1brown — это канал об анимированной математике во всех смыслах этого слова. Как всегда, если Вы хотите оставаться в курсе новых видео, то подписывайтесь: 3b1b.co/subscribe
One technical note: Its possible to have fractals with an integer dimension. The example to have in mind is some *very* rough curve, which just so happens to achieve roughness level exactly 2. Slightly rough might be around 1.1-dimension; quite rough could be 1.5; but a very rough curve could get up to 2.0 (or more). A classic example of this is the boundary of the Mandelbrot set. The Sierpinski pyramid also has dimension 2 (try computing it!).
The proper definition of a fractal, at least as Mandelbrot wrote it, is a shape whose «Hausdorff dimension» is greater than its «topological dimension». Hausdorff dimension is similar to the box-counting one I showed in this video, in some sense counting using balls instead of boxes, and it coincides with box-counting dimension in many cases. But its more general, at the cost of being a bit harder to describe.
Topological dimension is something thats always an integer, wherein (loosely speaking) curve-ish things are 1-dimensional, surface-ish things are two-dimensional, etc. For example, a Koch Curve has topological dimension 1, and Hausdorff dimension 1.262. A rough surface might have topological dimension 2, but fractal dimension 2.3. And if a curve with topological dimension 1 has a Hausdorff dimension that *happens* to be exactly 2, or 3, or 4, etc., it would be considered a fractal, even though its fractal dimension is an integer.
See Mandelbrots book «The Fractal Geometry of Nature» for the full details and more examples.
— 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if youre into that).
A brief intro to the main ideas behind How Bitcoin Works, including how money is transferred, who keeps track of it, and how the whole thing is secured. Want more? Check out my new in-depth course on the latest in Bitcoin, Blockchain, and a survey of the most exciting projects coming out (Ethereum, etc): app.pluralsight.com/library/courses/bitcoin-decentralized-technology
Lots of demos on how to buy, send, store (hardware, paper wallet). how to use javascript to send bitcoin. How to create Ethereum Smart Contract, much more.
Come funzionano i Bitcoin nel dettaglio. Translation by Simone Falchini, donation: 1MckLtN28UreyiTTB1s8HPx3fkEcJyw9j
Original video: www.youtube.com/watch?v=Lx9zgZCMqXE