Famously beautiful, the Mandelbrot Set is all about complex numbers. Featuring Dr Holly Krieger from MIT. More links & stuff in full description below ↓↓↓ The next part is on Numberphile2 at: http://youtu.be/oCkQ7WK7vuY Animation courtesy of team fresh. Check out more at: http://hd-fractals.com — Music: Alan Stewart. Support him at http://bit.ly/1sdwTHF More videos with Holly

Google asked this problem as an interview question. If the probability of seeing a car on the highway in 30 minutes is 0.95, what is the probability of seeing a car on the highway in 10 minutes? (assume a constant default probability) The video presents a solution. Blog post: http://wp.me/p6aMk-4Qk Sources 140 Google Interview Questions

Banks, Facebook, Twitter and Google use epic numbers – based on prime factors – to keep our Internet secrets. This is RSA public-key encryption. More links & stuff in full description below ↓↓↓ Gold Vault: https://youtu.be/CTtf5s2HFkA This video features Dr James Grime (http://singingbanana.com/). Message from James: “Thanks to Dr Chris Hughes of the University of

We’re talking pretty big numbers here… And an interesting idea about what it’d be like traveling in a Googolplex-sized Universe! More links & stuff in full description below ↓↓↓ With Antonio (Tony) Padilla and Ria Symonds from the University of Nottingham. About the brown paper: http://periodicvideos.blogspot.com/2012/02/brown-paper-question.html NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets:

You have a full 12 liter jug and empty 5 and 8 liter jugs. Can you measure exactly 6 liters? This problem dates to 1484 and was posed in the context of a milkman making a home delivery to a customer. The story goes this riddle so delighted Simeon Denis Poisson as a young boy

When is n² + 45 equal to a perfect square, for n a positive integer? I received this MathCounts problem by email from Bill by email. Can you figure it out? Watch the video for a solution. My blog post for this video https://wp.me/p6aMk-5i0 If you like my videos, you can support me at Patreon:

Ron Graham explains the number which takes his name… More links & stuff in full description below ↓↓↓ Graham’s Number (Numberphile T-Shirt): http://bit.ly/Grahams_T-Shirt See him discuss how big it is: http://youtu.be/GuigptwlVHo Extra footage here: http://youtu.be/rGWuimr5CGQ And our original Graham’s Number video: http://youtu.be/XTeJ64KD5cg Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile

You can multiply two numbers if you know how to double, halve, and add up numbers. This is really interesting: basically the Egyptians were using binary multiplication! Watch the video to see how it works. READ why this method works: http://mindyourdecisions.com/blog/2014/08/27/the-egyptian-method-russian-peasant-multiplication-video-and-a-proof/#.U_5I5vldV8E WATCH how ancient Egyptians divided numbers: https://www.youtube.com/watch?v=bKqQGISplMo This method is documented in the Rind

Fermat’s “Little” Theorem is great – but beware of Fermat Liars and tricky Carmichael Numbers. More links & stuff in full description below ↓↓↓ Continues at: http://youtu.be/HvMSRWTE2mI Featuring Dr James Grime – https://twitter.com/jamesgrime Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the

In a square, a line is drawn from the bottom left corner with length 12 to the interior of the square. From the end of that line, a perpendicular is drawn going up and left with length 3. From the end of that line, another perpendicular is drawn going up and right with length 9.

A million digits of Pi on one piece of paper (1.05 miles). More links & stuff in full description below ↓↓↓ More about how and why: http://youtu.be/99Welatppzk More Pi videos from Numberphile: http://bit.ly/PiPlaylist Film by Brady Haran Our thanks to HP and HSA Systems. Extra special thanks to Hugh McPartlan, Torben Dam Jensen, Jesper Hyldager

What is the value of x= 1/(1 + 1/(1 + 1/(1 + …)))? This continued infinite fraction has an interesting value! If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post, so you can follow me

The State of Indiana nearly passed a law which would have made Pi equal 3.2 – strange but true. More links & stuff in full description below ↓↓↓ More Pi videos from Numberphile: http://bit.ly/W4oDN1 This video features Dr James Grime – https://twitter.com/jamesgrime The video about squaring circles: https://www.youtube.com/watch?v=CMP9a2J4Bqw A note to potentially disgruntled viewers about

A bit about zero – including a discussion of its even-ness!? More links & stuff in full description below ↓↓↓ Featuring Dr James Grime (https://twitter.com/jamesgrime) and Professor Roger Bowley (University of Nottingham). NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Brady’s videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady’s

The 80/20 rule or Pareto principle comes up a lot in economics and business. But why does this pattern emerge? I show why using a paper clip experiment. Note: VSauce later made a video about Zipf’s law that uses this same experiment but does the math incorrectly. The long tail should be for the single

The Prisoner’s Dilemma is the most famous problem in game theory. Here I give a quick introduction to the problem. If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post, so you can follow me on

This is the higher quality version of how to multiply numbers by drawing lines. Get the Multiply By Lines Book! http://amzn.to/XRm7M4 If you like my videos, you can support me at Patreon: https://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post, so you can follow me

Featuring Tadashi Tokieda – more Tadashi videos at: http://bit.ly/tadashi_vids More links & stuff in full description below ↓↓↓ Tadashi Tokieda is a Professor of Mathematics at Stanford University (though this was filmed when he was at Cambridge, in the UK). Animation by Pete McPartlan. Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile

The quadratic formula is really useful, but its derivation is confusing to many. Like what is the point of “completing the square” anyway? In this video, I show how “completing the square” has a geometric interpretation–you are actually making the areas of two squares equal to each other! Blog post (text/image summary): http://wp.me/p6aMk-4kG You can

Why squaring the circle – the old-fashioned way – was found to be impossible? Numblr: http://numberphile.tumblr.com/ More links & stuff in full description below ↓↓↓ This video featuring Dr James Grime: https://twitter.com/jamesgrime The paper from this video on ebay – http://bit.ly/brownpapers NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by

In 1911, Srinivasa Ramanujan posed this problem involving an infinite nested radical (a never-ending expression that has square roots inside of square roots). Can you figure out how to simplify the equation? The video presents an intuitive solution. Technically it is necessary to prove the equation has a solution (the nested radical converges) because crazy

A number so epic it will collapse your brain into a black hole! Yet Tony Padilla and Matt Parker take the risk of discussing its magnitude. Watch with caution. More links & stuff in full description below ↓↓↓ See also our video about the Googol and Googolplex at: http://www.youtube.com/watch?v=8GEebx72-qs More about Matt and Tony at:

Dr James Grime discusses a type of number beyond the complex numbers, and why they are useful. Extra footage: https://youtu.be/ISbJ9S0fzwY More links & stuff in full description below ↓↓↓ Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute

This video gives a method to convert decimal numbers to binary numbers quickly. This is a variation of the remainder system that is typically taught in courses. I like this method because it gives the answer in the correct order from left to right. Proof of why it works: http://math.stackexchange.com/questions/86207/converting-decimalbase-10-numbers-to-binary-by-repeatedly-dividing-by-2 I also give a proof