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
Math
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
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 by from discussion inHomeworkHelp Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end
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 –
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
Students in the UK faced a similar question to this one. Don’t give up–U can solve it! Adapted from [GCSE Edexcel Further Math] How would you solve for x? byu/Gulags_Never_Existed inHomeworkHelp 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
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
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
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:
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
Johnny Ball discusses Archimedes and the volume of a sphere. Check out https://www.kiwico.com/Numberphile and get 50% off your first month of any subscription (sponsor) More links & stuff in full description below ↓↓↓ Johnny Ball: https://johnnyball.co.uk More Numberphile videos with Johnny Ball: http://bit.ly/Johnny_Ball Johnny Ball books: https://amzn.to/3v8Xxqx Numberphile is supported by the Mathematical Sciences Research
This was asked to students in 1801, but it is still a challenging and fun problem to solve to this day! Source See page 5, problem 24 https://archive.org/details/cambridgeproblem00cambuoft/page/4/mode/2up 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
A number of galactic proportions… See more #MegaFavNumbers on this playlist – https://bit.ly/MegaFavNumbers – and read below to contribute your own. More links & stuff in full description below ↓↓↓ See our full collection of video on the sum of three cubes at: http://bit.ly/SumOfCubes (*) the cube (which we depicted quite loosely and artistically, of
Happy #PiDay! When two of the hardest tests in the world cover the same problem, you know it’s a big deal. References Wikipedia article https://en.wikipedia.org/wiki/Proof_that_22/7_exceeds_%CF%80 Putnam exam 1968 A1 https://prase.cz/kalva/putnam/putn68.html JEE Advanced 2010 Paper Solutions Part-1 | IIT-JEE | Strategy, Tips, & Tricks | Paper Discussion (see around 55:30) https://youtu.be/Zz4buu5y7_8?t=3330 Proving 22/7 is greater than
Not all jokes are in base 10… More links & stuff in full description below ↓↓↓ With thanks to Audible – http://www.audible.com/numberphile (book details below) More jokes explained at: http://youtu.be/JJQWtGm3eIs Animation by by Pete McPartlan – http://www.petemcpartlan.co.uk Explanations by Matt Parker – http://www.standupmaths.com This video was posted during YouTube Comedy Week: http://yt.be/comedyweek Leave more joke
What is the average distance between two randomly chosen points in a square with a side length 1? The video presents how to estimate the answer and also derives the exact answer using integrals. Per suggestions in the comments, I have modified the title to indicate the difficulty level is VERY HARD (a college level
Partitions are a major part of the Ramanujan story (as shown in the new film about his life) – but what are they? More links & stuff in full description below ↓↓↓ Dr James Grime tackles the issue. Extra footage: https://youtu.be/ksHqQW94KlE More James Grime on Numberphile: http://bit.ly/grimevideos Young Tableau: https://youtu.be/vgZhrEs4tuk Shuffling: https://youtu.be/AxJubaijQbI James discusses Good
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:
This is adapted from the Mathematics Olympiad of Nepal (MOON). 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 make videos. Be
John H Conway on his love/hate relationship with his most “famous” invention. Conway playlist: http://bit.ly/ConwayNumberphile More on how he invented it at: http://youtu.be/R9Plq-D1gEk 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
University entrance exams and job interviews have asked questions similar to this problem. What is the area of the rectangle? What is the minimum area of the large triangle? Special thanks this month to: Jamal Jackson, Mike Robertson, Michael Anvari, Robert Zarnke, Fiona Harper, Kyle. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send
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
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
Can you solve this geometry problem? Thanks to Lucas from Brazil for the suggestion! Kangaroo Maths 2020 https://www.matematica.pt/en/docs/kangaroo/enunciados/2020/2020_Grade9-10.pdf Proof of inscribed angle theorem https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-inscribed-angles/a/inscribed-and-central-angles-proof 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
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!
Thanks to Devesh from India for the suggestion! A version of this problem was given in an Olympiad qualifying test. Socratic https://socratic.org/questions/a-root-a-b-root-b-183-a-root-b-b-root-a-182-find-9-5-a-b Math StackExchange https://math.stackexchange.com/questions/2405256/find-the-value-of-frac95ab-given-that-a-sqrtab-sqrtb-183-and-a Brainly https://brainly.in/question/3901575 Quora https://www.quora.com/Suppose-a-b-are-positive-real-numbers-such-that-a%E2%88%9Aa-+-b%E2%88%9Ab-183-a%E2%88%9Ab-+-b%E2%88%9Aa-182-How-do-we-find-9-5-a-+-b 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
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:
Professor Ron Graham discusses the famed Happy Ending Problem and Ramsey Theory. More Ron Graham Videos: http://bit.ly/Ron_Graham More links & stuff in full description below ↓↓↓ An extra little bit at: http://youtu.be/hnIBiIcuudU Graham’s Number: 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 tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported
Can you solve this geometry brain teaser? Note: I was emailed a similar problem but I am unable to locate the original source. It seems to be in the style of Bright Side quizzes, but often those are based on problems circulating. Please let me know if can identify the original source and I will
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:
This is a fun one! Sources National Museum of Mathematics tweet Can you solve this #math problem for #MathMonday? We will reveal the answer in 24 hours! Suppose there is a square ABCD with a point E on edge BC and a point F on edge CD such that the area of triangle ABE is
If an octagon with equal sides is cut from a rectangle with sides of 4 and 6, what is the side length of the octagon? It’s a pretty fun problem to work out! Adapted from suggestion on Twitter @preshtalwalkar a regular octagon cut from a rectangle length and breadth 6 and 8 cm. What is
George Dantzig, William Sidis, Srinivasa Ramanujan? Who was the real Good Will Hunting? More links & stuff in full description below ↓↓↓ Maths in Good Will Hunting: http://www.youtube.com/watch?v=iW_LkYiuTKE This video features Numberphile’s very own mathematics superstar – Dr James Grime. 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
Can you solve this interesting geometry problem? References Solution by “WAY TO GOVT JOB” on YouTube Stretched length of band https://www.thestudentroom.co.uk/showthread.php?t=1936482 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
It’s not so simple to solve for this simple answer. Thanks to all patrons! Special thanks this month to: Richard Ohnemus, Michael Anvari, Shrihari Puranik, Kyle. WolframAlpha Get Real with Wolfram|Alpha—Computing Roots https://www.wolframalpha.com/input/?i=cuberoot(8%2B3*sqrt(21))%2Bcuberoot(8-3*sqrt(21)) https://www.wolframalpha.com/input/?i=(8%2B3*sqrt(21))%5E(1%2F3)%2B(8-3*sqrt(21))%5E(1%2F3) 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 This is the only channel to feature math topics suggested by
This challenging geometry problem appeared on one of the hardest math competitions (the Putnam exam), and there is a neat way to solve it! The Putnam Exam has legendary difficulty: the average (median) score is usually 1 out of a possible 120 points. No calculators allowed though, and you have to prove everything very carefully.
Tadashi’s back (for the final video in this mini series) demonstrating the Kendama and some angular momentum. More links & stuff in full description below ↓↓↓ Tadashi Tokieda will be back on Numberphile soon. Here’s a playlist of his videos: http://bit.ly/tadashi_vids Kendama also known as bilboquet or boliche or bolero. Video by Brady Haran and
15-year old Joseph Rosenfeld thought he spotted an error in the Boston Museum of Science. The exhibit Mathematica has a sign that says the golden ratio is (√5 – 1)/2. He remembered and checked online that the golden ratio is supposed to have a positive symbol, (√5 + 1)/2. He left a note for the
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
L-Functions are likely to play a key role in proving the Riemann Hypothesis, says Professor Jon Keating from the University of Bristol. More links & stuff in full description below ↓↓↓ L-Function & Modular Form database: http://www.lmfdb.org Prime Number and Riemann Hypothesis playlist: http://bit.ly/primevids Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook:
Can you solve for the area of the square and the length of the tangent line? Special thanks this month to Fiona Harper, Kyle, Mike Robertson, Michael Anvari, Robert Zarnke. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Adapted from a puzzle by Twitter @Cshearer41 (Catriona Agg) A semicircle and quarter circle inside a square. How
Tadashi Tokieda is back, this time with Moiré Patterns. More with Tadashi: http://bit.ly/tadashi_vids More links & stuff in full description below ↓↓↓ Out thanks also to our Patreon supporters, especially: Jeff Straathof Ken Baron Today I Found Out Roman Urbanovski Joanna & Mehdi Christian Cooper Peggy Y John Buchan Bill Shillito Andrzej ‘Yester’ Fiedukowicz Ripta
Problem 1: Two ladders are criss-crossed against walls of height 3 and 5. At what height do they intersect? Problem 2: I take 3 hours to complete a job, and you take 5 hours to do the same job. How long does it take if we work together? This video demonstrates that both problems have
Just a quick number trick with Dr James Grime. More links & stuff in full description below ↓↓↓ 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 latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts:
This problem went viral after it appeared on a Math Olympiad test for talented students in Singapore. It’s not a trick question! Here’s the problem, which I have very slightly re-worded for clarity. Blog post (detailed text explanation): http://mindyourdecisions.com/blog/2015/04/14/when-is-cheryls-birthday-answer-to-viral-math-puzzle/ Source: https://www.facebook.com/kennethjianwenz/photos/a.173663129479243.1073741827.167504136761809/385751114937109/?type=1&theater Official Solution: http://mothership.sg/2015/04/p5-logic-question-is-actually-a-math-olympiad-question-for-sec-3-and-4-students/ Albert and Bernard have just become friends with Cheryl, and they