# Math

If a semicircle and its flipped copy are placed side by side, how much distance do they span from end to end? This is a neat problem adapted from a Mathematical Olympiad Qualifying Test in the Philippines. Can you figure it out? Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos).

Featuring Hannah Fry discusses Train Graphs. More links & stuff in full description below ↓↓↓ Hannah’s website, including links to her many and varied projects… and latest books: https://hannahfry.co.uk Her latest book (with Adam Rutherford) is the Complete Guide to Absolutely Everything (Abridged): https://amzn.to/30Mr6UE Hannah on Numberphile: http://bit.ly/hannah_vids Hannah on the Numberphile podcast: https://youtu.be/KKCjQWmUwv8 Numberphile

Matt Parker talks about numbers – as he often does. His book “Humble Pi” is at: http://bit.ly/Humble_Pi More links & stuff in full description below ↓↓↓ The book on Amazon: https://amzn.to/2NKposg Numberphile podcast is on your podcast player. Or the website is: https://www.numberphile.com/podcast And it’s on YouTube too: http://bit.ly/Numberphile_Pod_Playlist The Knight’s Tour T-Shirt is in

Thanks to Jumar for the suggestion! Can you solve this interesting geometry problem? 0:00 Problem 1:10 Similar triangles 2:29 Solution Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a commission

Langton’s Ant – starring Katie Steckles (and Audrey). More links & stuff in full description below ↓↓↓ Extra footage: https://youtu.be/oTssNuDEkSc The 104-steps: https://youtu.be/xU072T4V12A John Conway videos: http://bit.ly/ConwayNumberphile Support us on Patreon: http://www.patreon.com/numberphile Katie Steckles website: http://bit.ly/stecks_web Audrey: https://www.facebook.com/AudreyAdorable One of many online simulators: http://rossscrivener.co.uk/projects/langtons-ants/ Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook:

Thanks to Ben Craft for sending me this problem and its solution! Find a value of x such that (3 + 4)(3^2 + 4^2)(3^4 + 4^4)(3^8 + 4^8)(3^16 + 4^16)(3^32 + 4^32) = 4^x – 3^x. There’s a really neat trick that simplifies the problem like magic! Thanks to Nar235 and Jonathan Love for finding

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 http://www.impactinterview.com/2009/10/140-google-interview-questions/ http://www.businessinsider.com/answers-to-15-more-google-interview-questions-that-will-make-you-feel-stupid-2010-11#if-the-probability-of-observing-a-car-in-30-minutes-on-a-highway-is-095-what-is-the-probability-of-observing-a-car-in-10-minutes-assuming-constant-default-probability-2 If you

The 1947 Stanford Competitive Examination included a version of this problem. Reference https://www.cut-the-knot.org/Outline/Arithmetic/DivisionBy72.shtml Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to

Thanks to George Tan for suggesting this problem! It is from the 2019 SPM paper in Malaysia. Many students cried after taking the exam, and many teachers found the problems to be very challenging as well. (This means the problems were hard given the syllabus and expectations of the exam–no need to let us know

I received many requests for this challenging problem. Can you solve it? Thanks to Toli for the suggestion! Geometry solution in method 1 http://128.192.17.191/EMT668/EMAT6680.F99/Estes/15degrees/15degreesgeometric.html Another geometry solution http://128.192.17.191/EMT668/EMAT6680.F99/Estes/15degrees/solution2.html Trigonometry solution http://128.192.17.191/EMT668/EMAT6680.F99/Estes/15degrees/15degreestrigonometric.html Go Geometry discussion https://gogeometry.blogspot.com/2009/11/problem-395-square-15-degree.html https://drive.google.com/file/d/1A0Az5nJ9wGBwcM2F4gQY2dSfeKJZ1gSS/view Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I

This is a nice little logic puzzle from Terry Stickels! Books by Terry Stickels (including “Contemporary Brainteasers”) http://www.terrystickels.com/books.html Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on

Professor Tony Padilla is back with another epic number. Our Big Number playlist of previous videos: http://bit.ly/Big_Numbers More links & stuff in full description below ↓↓↓ Busy Beavers on Computerphile: https://youtu.be/CE8UhcyJS0I With thanks to Agustín Rayo himself. Read more from Prof Rayo at: http://web.mit.edu/arayo/www/bignums.html And see his website at: https://arayo.scripts.mit.edu/home/ Tony Padilla: https://twitter.com/DrTonyPadilla Numberphile is

Photomath can’t solve this, and neither can Mathway, Symbolab, or Desmos. Can you? I explain how you can. A similar problem was given to high school students in Massachusetts, and you really have to know what you’re doing to figure it out. Thanks to all patrons! Special thanks this month to: Shrihari Puranik Richard Ohnemus

An evil warden holds you prisoner, but offers you a chance to escape. There are 3 doors A, B, and C. Two of the doors lead to freedom and the third door leads to lifetime imprisonment, but you do not which door is what type. You are allowed to point to a door and ask

Tadashi is back, this time looking at drooping paper (and toilet paper). More links & stuff in full description below ↓↓↓ Subscribe to Numberphile and never miss a floppy paper video: http://bit.ly/Numberphile_Sub Playlist of Tadashi Tokieda videos: http://bit.ly/tadashi_vids Pizza and Gaussian curvature: https://youtu.be/gi-TBlh44gY Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile

An exciting paper about gaps between prime numbers – a step closer to proving the twin prime conjecture. More links & stuff in full description below ↓↓↓ Extra footage at http://youtu.be/D4_sNKoO-RA The proof was published by Yitang “Tom” Zhang from the University of New Hampshire. We’re discussing it in simple terms with Numberphile regulars –

What is 7×8? This video teaches how you can use your hands to multiply two numbers between 6 and 10 using your fingers. Here’s the reason the method works: https://www.youtube.com/watch?v=eEao6-F7fz8 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

Archimedes’s famous Cattle Problem had a truly epic solution. Featuring Alex Bellos. More links & stuff in full description below ↓↓↓ Alex Bellos: http://www.alexbellos.com More Alex videos on Numberphile: http://bit.ly/Bellos_Playlist So You Think You’ve Got Problems by Alex Bellos Amazon: https://amzn.to/2KR9Get Signed copies via MathsGear:http://bit.ly/BellosProblemsSigned More Alex books: https://amzn.to/2KQTc5Y The Cattle Problem by AH Bell:

This problem went viral because even teachers had trouble solving it. It even got covered in television news! Can you figure it out? References BlackPenRedPen Twitter https://twitter.com/blackpenredpen/status/1284719356799115264 BlackPenRedPen video (English) BlackPenRedPen video (Chinese) China Times News Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like

Check our sponsor The Great Courses Plus (free trial): http://ow.ly/j5cB30hIvm2 This video features Cliff Stoll. More links & stuff in full description below ↓↓↓ More Cliff Stoll videos: http://bit.ly/Cliff_Videos Buy a Klein Bottle from Cliff – it’s an experience: http://www.kleinbottle.com Discuss this video on Brady’s subreddit: https://redd.it/96x6c4 Numberphile is supported by the Mathematical Sciences Research

Many students in the UK had difficulty with a similar problem on the GCSE exam. What’s the rectangle’s area, given the three circles are identical with radius r? Watch the video to learn how to solve this problem. Sources Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g Send me your favorite puzzles/suggestions by

The knight’s tour and magic knight’s tour. More links & stuff in full description below ↓↓↓ The first magic tour has an error (my fault in animation) with 62 and 64 transposed…. See here: http://periodicvideos.blogspot.co.uk/2014/01/oops.html Brown papers: http://bit.ly/brownpapers Some good knight’s tour links: Great overview by Ben Hill and Kevin Tostado: http://bit.ly/1hYHoLE Notes and huge

The ancient Babylonians used a number system with base 60 (sexagesimal). More links & stuff in full description below ↓↓↓ Tablet image courtesy of Bill Casselman and Yale Babylonian Collection – more at http://www.math.ubc.ca/~cass/Euclid/ybc/ybc.html This video features Thomas Woolley – he tweets at https://twitter.com/#!/thomasewoolley NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe:

The famed Poincaré Conjecture – the only Millennium Problem cracked thus far. More links & stuff in full description below ↓↓↓ Ricci Flow (used to solve the problem): http://youtu.be/hwOCqA9Xw6A Riemann Hypothesis: http://youtu.be/d6c6uIyieoo Extra interview footage with Jim Isenberg: http://youtu.be/7eJleW0JcKg Grigori Perelman’s paper: http://bit.ly/perelmanpaper Discussed here by Katie Steckles and James Isenberg. Support us on Patreon:

Tadashi Tokieda puts $20 on the line… More links & stuff in full description below ↓↓↓ More Tadashi videos: http://bit.ly/tadashi_vids Paperclips: https://youtu.be/wGkvyN6s9cY Video by Brady Haran and Pete McPartlan (animations by Pete) 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

Albert Einstein was challenged with a simple riddle in a 1934 correspondence with the psychologist Max Wertheimer. Can you figure it out? Thanks to all patrons! Special thanks to: Shrihari Puranik, Richard Ohnemus, Michael Anvari, Kyle. We are the only channel to feature math topics suggested by people around the world. Support on Patreon to

Hippocrates of Chios solved this, nearly 100 years before Euclid even wrote The Elements, and before we knew the exact formula for the area of a circle. This is said to be the first precise mathematical of the area between two curved lines. Learn how he solved for the area of a crescent-shaped lune (same

Fields Medallist and math “celebrity” Cédric Villani is famous for wearing ornate spiders on his lapel. More Villani videos: http://bit.ly/Villani_Videos Cédric Villani website: http://cedricvillani.org His book Birth of a Theorem (Amazon): http://bit.ly/BirthOfATheorem Villani talks about his Fields Medal: https://youtu.be/Vp3sgYKULp0 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by

Featuring Professor Howard Masur from the University of Chicago. Filmed at the Mathematical Sciences Research Institute (MSRI). Part 2 of this interview: https://youtu.be/AGX0cLbHaog Patreon: http://www.patreon.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of

Can you solve this incredibly difficult calculus question? I had a lot of fun solving this one! Special thanks this month to: Kyle, Mike Robertson, Michael Anvari. Robert Zarnke, Fiona Harper. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Adapted from Comment from discussion PhysicsHelpBernoulli’s comment from discussion "[12th grade math] What number would n have

Squarespace: http://www.squarespace.com/numberphile More links & stuff in full description below ↓↓↓ More linguistics on Numberphile: http://youtu.be/SbZCECvoaTA Billion and Trillion: http://youtu.be/C-52AI_ojyQ Tom Scott on numbers and linguistics – a discussion with spans counties, countries, continents and the far reaches of space. Tom’s own channel is: https://www.youtube.com/user/enyay Art and animation by Pete McPartlan http://www.petemcpartlan.co.uk Support us on

A chat about some of the ways legendary physicist Richard Feynman cracked safes (filing cabinets) at Los Alamos during the Manhattan Project. More links & stuff in full description below ↓↓↓ Discussed by Professor Roger Bowley. My Favourite Scientist on Feynman: http://www.youtube.com/watch?v=qoYWfytx5QA Feynman Diagrams: http://www.youtube.com/watch?v=3bbJeMBHq0g Enigma: http://www.youtube.com/watch?v=G2_Q9FoD-oQ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile

I had a lot of fun solving this one, and I think you will too! 0:00 Problem 0:49 Hints 4:12 Solution Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a

Beautiful Dragon Curves, Fractals and Jurassic Park. Featuring Rob Eastaway. More links & stuff in full description below ↓↓↓ Rob’s website: http://www.robeastaway.com/ Thanks to Matthew Ward and Faraz Barzideh who helped Brady out with some curves! The book Jurassic Park is by the late Michael Crichton. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets:

Your math teacher and friends will be confused, but you’ll look like a genius when you solve multiplication problems with this unusual math trick. Source: I read about this trick from a math book first published in 1956. (Rapid Math Without A Calculator by Frederick Collins). If you like my videos, you can support me

This problem is adapted from an Oxford University admissions question. They say if you can solve this in your head, you are a genius 😉 Alex Bellos’s column on The Guardian https://www.theguardian.com/science/2021/jul/12/did-you-solve-it-oxford-university-admissions-questions Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas!

Johnny Ball on Russian and Egyptian Multiplication. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More on Johnny Ball, including his books and live shows: https://www.johnnyball.co.uk Russian multiplication is also known as Ethiopian multiplication. Why Use Binary? (on Computerphile) – https://youtu.be/thrx3SBEpL8 Discuss on

A triangle with sides of 4, 3, and 5 is drawn inside a square as shown. What is the length of the square’s side? It’s a fun little geometry problem! Sources https://www.instagram.com/p/Btw9ZfyBz5w/ http://mathhelpforum.com/geometry/236852-area-square-right-triangle-inside.html Egyptian Proverb http://oaks.nvg.org/egyptian-proverbs.html Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Why

French numbers can pose problems for non-native speaker – especially when you move beyond 70. Also discussing problems with phone numbers and commas! More links & stuff in full description below ↓↓↓ Featuring Dr Paul Smith from the University of Nottingham. The French and marks out of 20: http://www.youtube.com/watch?v=QzrRkhU248A A little extra unlisted bit from

Three chords are drawn in a circle, spaced 30 degrees apart from the same vertex. If the left chord is 10, and the right chord is 12, what is the length of the middle chord? Wow! The channel “Freedom Mathematics” did a general case of the chord progression puzzle. The general problem is quite complicated!

Infographics are not new.. in 1862 Charles Joseph Minard created a much-praised infographic depicting Napoleon’s invasion of Russia in 1812. More links & stuff in full description below ↓↓↓ This video features Dr James Grime – http://singingbanana.com More of James on Numberphile: http://bit.ly/grimevideos Here is the info graphic: http://en.wikipedia.org/wiki/File:Minard.png A book coming soon about the

Featuring Ben Sparks discussing the Mandelbrot Set (and Julia Sets). Catch a more in-depth interview with Ben on our Numberphile Podcast: https://youtu.be/-tGni9ObJWk More links & stuff in full description below ↓↓↓ More videos with Ben: http://bit.ly/Sparks_Playlist Ben Sparks website: https://www.bensparks.co.uk And on Twitter: https://twitter.com/sparksmaths Holly Krieger has done a few Mandelbrot videos on Numberphile… The

This is a fun little geometry problem. Source Bilal Sarımeşeli tweet #math #geometry #teachertwitter #questiontime Find the radius of the circle. pic.twitter.com/C1l5P2iAvN — Bilal Sarımeşeli (@bilalsarimeseli) September 26, 2019 Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to

Sequence guru Neil Sloane on a sequence which puzzled him – until he spotted the mistake! More links & stuff in full description below ↓↓↓ More Neil Sloane videos: http://bit.ly/Sloane_Numberphile The OEIS: https://oeis.org Hanny’s Voorwerp: https://youtu.be/RDr6bSB6Vlg Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a

Three squares are placed in a row. Connect the bottom left corner of each square to the top right corner of the third square, forming angles with measures a, b, c with the horizontal. What is the sum of a, b, and c? Many people requested this problem, and I thank Roberto O. and Cardist

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