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Videos uploaded by user “3Blue1Brown” for the 2018
How pi was almost 6.283185...
 
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Happy pi day! Did you know that in some of his notes, Euler used the symbol pi to represent 6.28..., before the more familiar 3.14... took off as a standard? Plushie creatures now available: http://3b1b.co/store Why? Well, people asked, and what better way to celebrate pi day? The idea for this video, as well as the live shots, came from Ben Hambrecht, with the writing and animating done by Grant Sanderson. Special thanks to: - University Library Basel, for letting us rummage through their historical collection - Martin Mattmüller from the Bernoulli-Euler center for helpful discussion - Michael Hartl, author of the Tau Manifesto, for pointing us to obscure references - Library of the Institut de France Cinematographer: Eugen Heller Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown https://soundcloud.com/vincerubinetti/ ------------------ 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 you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 371924 3Blue1Brown
But what is the Fourier Transform?  A visual introduction.
 
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An animated introduction to the Fourier Transform, winding graphs around circles. Supported by viewers: https://www.patreon.com/3blue1brown Special thanks to these Patrons: http://3b1b.co/fourier-thanks Follow-on video about the uncertainty principle: https://youtu.be/MBnnXbOM5S4 Puzzler at the end by Jane Street: https://janestreet.com/3b1b Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/ ------------------ 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 you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 1088898 3Blue1Brown
What they won't teach you in calculus
 
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A visual for derivatives which generalizes more nicely to topics beyond calculus. Problem-driven learning by Brilliant: https://brilliant.org/3b1b Essence of calculus series: http://3b1b.co/calculus Special thanks to the following patrons: http://3b1b.co/alt-calc-thanks https://www.patreon.com/3blue1brown Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown https://soundcloud.com/vincerubinetti/ ------------------ 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 you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown
Views: 700109 3Blue1Brown
Why is pi here?  And why is it squared?  A geometric answer to the Basel problem
 
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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 kind subset of you who choose to contribute for each new video: https://www.patreon.com/3blue1brown The content here was based on a paper by Johan Wästlund http://www.math.chalmers.se/~wastlund/Cosmic.pdf Brilliant's principles list that I referenced: https://brilliant.org/principles/ Special thanks to these Patrons: http://3b1b.co/basel-thanks Check out Mathologer's video on the many cousins of the Pythagorean theorem: https://youtu.be/p-0SOWbzUYI On the topic of Mathologer, he also has a nice video about the Basel problem: https://youtu.be/yPl64xi_ZZA A simple Geogebra to play around with the Inverse Pythagorean Theorem argument shown here. https://ggbm.at/yPExUf7b Some of you may be concerned about the final step here where we said the circle approaches a line. What about all the lighthouses on the far end? Well, a more careful calculation will show that the contributions from those lights become more negligible. In fact, the contributions from almost all lights become negligible. For the ambitious among you, see this paper for full details. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown https://soundcloud.com/vincerubinetti/ ------------------ 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 you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 581740 3Blue1Brown
The more general uncertainty principle, beyond quantum
 
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The Heisenberg uncertainty principle is just one specific example of a much more general, relatable, non-quantum phenomenon. Apply to work at one of my favorite math education companies: http://aops.com/3b1b Special thanks to the following Patrons: http://3b1b.co/uncertainty-thanks You are the ones making this possible: http://3b1b.co/support For more on quantum mechanical wave functions, I highly recommend this video by udiprod: https://youtu.be/p7bzE1E5PMY Minute physics on special relativity: https://youtu.be/1rLWVZVWfdY Main video on the Fourier transform https://youtu.be/spUNpyF58BY Louis de Broglie thesis: http://aflb.ensmp.fr/LDB-oeuvres/De_Broglie_Kracklauer.pdf More on Doppler radar: Radar basics: https://www.eetimes.com/document.asp?doc_id=1278808 There's a key way in which the description I gave of the trade-off in Doppler radar differs from reality. Since the speed of light is so drastically greater than the speed of things being detected, the Fourier representation for pulse echoes of different objects would almost certainly overlap unless it was played for a very long time. In effect, this is what happens, since one does not send out a single pulse, but a whole bunch of evenly spaced pulses as some pulse repetition frequency (or PRF). This means the Fourier representation of all those pulses together can actually be quite sharp. Assuming a large number of such pulses, it will look like several vertical lines spaced out by the PRF. As long as the pulses are far enough apart that the echoes of multiple objects on the field from different targets don't overlap, it's not a problem for position determinations that the full sequence of pulses occupies such a long duration. However, the trade-off now comes in choosing the right PRF. See the above article for more information. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown https://soundcloud.com/vincerubinetti/ ------------------ 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 you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 404631 3Blue1Brown
Solving 2D equations using color, a story of winding numbers and composition
 
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An algorithm for numerically solving certain 2d equations. Brought to you by...you! https://patreon.com/3blue1brown Special thanks to these supporters: http://3b1b.co/winding-thanks Even though we described how winding numbers can be used to solve 2d equations at a high level, it's worth pointing out that there are a few details missing for if you wanted to actually implement this. For example, in order to determine how often to sample points, you'd want to have some bounds on the rate at which the direction of the output changes. We will perhaps discuss this more in a follow-on video! Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown https://soundcloud.com/vincerubinetti/ ------------------ 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 you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown
Views: 325082 3Blue1Brown
Why does this product equal π/2?  A new proof of the Wallis formula for π.
 
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A new and more circularly proof of a famous infinite product for pi. Try out Udacity: https://udacity.com/3b1b Here's supplemental blog post, expanding some of the rigor of this proofs, along with other interesting tidbits about surrounding topics that we didn't fit into the video: https://www.3blue1brown.com/sridhars-corner/2018/4/17/wallis-product-supplement-dominated-convergence Special thanks to the following Patreon supporters: http://3b1b.co/wallis-thanks If you also want to support videos like these, visit https://www.patreon.com/3blue1brown Another approach to this product by Johan Wästlund: http://www.math.chalmers.se/~wastlund/monthly.pdf With more from Donald Knuth building off this idea: https://apetresc.wordpress.com/2010/12/28/knuths-why-pi-talk-at-stanford-part-1/ Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/a... https://soundcloud.com/vincerubinetti/ ------------------ 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 you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown
Views: 218685 3Blue1Brown
Divergence and curl | Fluid flow with complex functions, part 1
 
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Intuitions for divergence and curl, and where they come up in physics. Brought to you by you: https://www.patreon.com/3blue1brown Thoughts on going sponsor-free: https://www.patreon.com/posts/19586800 Special thanks to these supporters: http://3b1b.co/divcurl-thanks My former work on divergence and curl at Khan Academy: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives For more fun fluid-flow illustrations, which heavily influenced how I animated this video, I think you'll really enjoy this site: https://anvaka.github.io/fieldplay/ Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown https://soundcloud.com/vincerubinetti/ ------------------ 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 you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown
Views: 78621 3Blue1Brown

Bitcoin client types
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When transferring lots of currency you should be careful were you do it to find the best rates. Negotiate hard and receive the very best rate you`re able to. The lower an individual credit rating, the greater her APR interest rate will be.
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Utilizing AI algorithms, it will not merely improve itself but can also supply you with precious info about your customers. Understand their terms and legal info, then choose one that you`re comfortable and confident with. Secondly, it`s crucial that you collect as much info and insight as you`re able to.

The miners are interested in finding a nonce which will create a hash with certain characteristics. Lastly, they have to find a random value that they included in the header, which makes the computed hash over that header a value below a particular target. In other words, they do not have to agree to change the protocol. Though there are a few gold diggers attempting to fill their pockets and certain projects that aren`t viable and shouldn`t be encouraged in any way. For users running a complete node, it is a fairly painless procedure to upgrade the software to the newest version. The process of locating a new block to extend the blockchain is known as mining. Proof-of-Work systems utilize cryptographic hashing algorithms to create the action of mining a block a complicated computation. Our software is totally incompatible with altcoins. Changes and modifications to how that it works need to be approved by consensus and every CPU gets a vote. To start with, it`s essential to realize that hardware wallet users control entirely their private keys. Whether you`re bullish or bearish on Bitcoin Gold, you ought not lose your coins as a result of careless mistakes! On the 1 hand, it may result in making a coin that solves all the pending issues. There`s no currency or digital asset named Bitcoin Core. Bitcoin Cash increases the range of transactions that may be processed per block. You could send any quantity of money, any place in the Earth, almost at no cost. You`ve made some great money already on the market, but you want more. For a wealthy individual, BTC`s price premium may be viewed as a plus. For someone without lots of money, BCH`s low price may look like a great deal for Bitcoin. If you have some concerns about the worth of Bitcoin after all forks, you need to be ready for a drop. The distinction is that not all of these suffer the chain split. The primary problem is Bitcoin imposes a hard limit on the magnitude of a block, the location where transaction information becomes stored. The end result is many straightforward wallets, called SPV wallets and very commonly found on your phone, will be quite confused about which chain is Bitcoin. In Bitcoin, the most important reason is known as the network effect.