Math

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

The anti-twister mechanism is mesmerizing. #shorts Belt Trick, JasonHise CC0 (public domain dedication) https://commons.wikimedia.org/wiki/File:Belt_Trick.gif https://en.wikipedia.org/wiki/Plate_trick https://en.wikipedia.org/wiki/Anti-twister_mechanism JasonHise Youtube video belt trick animation Robin Saunders (https://mathoverflow.net/users/4336/robin-saunders), Proofs without words, URL (version: 2016-12-29): https://mathoverflow.net/q/258356 proofs without words mathoverflow https://mathoverflow.net/questions/8846/proofs-without-words Let’s Twist Again – Chubby Checker https://youtu.be/Frw7U5X8dhg

Astronomer Dr Meghan Gray on leap years and Julian dates. More links & stuff in full description below ↓↓↓ Meghan is making a “guest appearance” on Numberphile and is more familiar to viewers of our sister channels DeepSkyVideos and Sixty Symbols. DeepSkyVideos: https://www.youtube.com/user/deepskyvideos Sixty Symbols: https://www.youtube.com/user/sixtysymbols NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets:

Trigonometry from a circle #shorts Animation based on https://math.stackexchange.com/questions/733754/visually-stunning-math-concepts-which-are-easy-to-explain https://www.khanacademy.org/computer-programming/circle/4597064320155648 Song credit Post Malone – Circles https://youtu.be/wXhTHyIgQ_U

Visual explanation of the difference of squares formula from math class The Difference – The Wallflowers https://youtu.be/5qSAMtomFvk

Thanks to Reio in Romania for emailing me this fun problem! What is the area? This puzzle was shared with the tagline “you should be able to solve this.” Solution to 5th grade Chinese challenge problem My blog post for this video https://wp.me/p6aMk-82G Reference Math problem from anime Steins;Gate https://math.stackexchange.com/questions/798367/area-of-a-part-of-a-square Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions

This was given to 13-14 year olds in Russia. Thanks to Egor Nazarov for suggesting this problem! Thanks to all patrons! Special thanks this month to Kyle, Michael Anvari, Richard Ohnemus, Shrihari Puranik. Get early access to videos and support the channel on Patreon https://www.patreon.com/mindyourdecisions Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video).

Continuing to talk Infinitesimals, this time with Dr James Grime. See last week’s video: https://youtu.be/BBp0bEczCNg More links & stuff in full description below ↓↓↓ Dividing by Zero: https://youtu.be/BRRolKTlF6Q James Grime: http://singingbanana.com 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

This is a fun little geometry problem! DataGenetics http://datagenetics.com/blog/november22016/index.html How to solve the shape-shifting triangle 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 are some comments before the video is published? Get early access and support the channel on Patreon https://www.patreon.com/mindyourdecisions If you buy

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:

Some people say this is “how the Japanese multiply.” Others say this is “Vedic Math.” I’m not sure of the origin, but this is a visual way to multiply two numbers and it does work. The video also shows how to use the same method to multiply algebraic expressions like (x + 2)(x + 3).

Some say only geniuses can solve this one. The video presents a sentence and asks you to identify all of the five errors. Can you figure it out? It is a tricky but I think many of you are clever enough to figure it out. My blog post for this video: https://wp.me/p6aMk-5iC If you like

This is a math joke from Wikipedia’s article on mathematical fallacies: https://en.wikipedia.org/wiki/Mathematical_fallacy#Howlers Thanks to Jetx 47 for the reference to Wikipedia. #Shorts 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 purchase through these links, I may be compensated

This one stumped me. Can you figure it out? #shorts Source https://matchstickpuzzles.blogspot.com/2021/05/635-one-is-not-equal-to-six.html 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 purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I

Fun with toothpicks. Featuring Neil Sloane. More links & stuff in full description below ↓↓↓ Neil Sloane is the founder of the On-Line Encyclopedia of Integer Sequences: https://oeis.org Play with the toothpick simulator: http://oeis.org/A139250/a139250.anim.html The Toothpick Sequence and Other Sequences from Cellular Automata by David Applegate, Omar E. Pol, and N. J. A. Sloane: https://arxiv.org/abs/1004.3036

They say “You should be able to solve this,” but the internet can’t agree on the answer! What do you think? #shorts MindYourDecisions poll results https://www.youtube.com/post/Ugzv_XryKGRUCCNDluN4AaABCQ The Moscow Puzzles (problem 37) by Boris A. Kordemsky, edited by Martin Gardner http://www.math.cmu.edu/~bkell/21110-2010s/algebra-puzzles.pdf https://www.doverpublications.com/mathsci/0718/d/270785_Easy_Answers.pdf Related memes https://www.physicsforums.com/threads/math-puzzle.477209/ https://knowyourmeme.com/forums/just-for-fun/topics/14038-you-really-should-be-able-to-solve-this Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 If you buy from the links below I

Why is it problematic to measure the length of coastline? Featuring Steve Mould: https://twitter.com/MouldS More links & stuff in full description below ↓↓↓ With thanks to the Ordnance Survey: http://www.ordnancesurvey.co.uk 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

The recent GCSE exam left many students baffled. Here’s how to solve one of more challenging questions. Thanks to Joe and Rob for the suggestion! The ‘impossible’ question on GCSE exam that had 16-year-olds across the country stumped https://www.manchestereveningnews.co.uk/news/greater-manchester-news/impossible-question-gcse-exam-16-24021464 Thousands of kids left baffled by ‘impossible’ GCSE question they claim can’t be solved – do

This illusion has fooled millions around the world. Here is a mathematical explanation of why it works. #shorts 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 purchase through these links, I may be compensated for purchases made on

Johnny Ball is back talking about Hippocrates, Lunes, and a Fancy Q. More links & stuff in full description below ↓↓↓ Johnny Ball’s website: https://johnnyball.co.uk More Johnny on Numberphile: https://bit.ly/Johnny_Ball An earlier Lunes video we did with Barry Mazur: https://www.youtube.com/watch?v=n_FsAwvxBI8 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported

Thanks to Arber for the suggestion! If AB = AC = AD and BAC = 50 degrees, what is the measure of BDC? This is a nice geometry problem! #Shorts 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

Catch a more in-depth interview with Ben Sparks on our Numberphile Podcast: https://youtu.be/-tGni9ObJWk Get 10% off at Squarespace: https://www.squarespace.com/numberphile More links & stuff in full description below ↓↓↓ Ben Sparks Twitter: Tweets by SparksMaths More of Ben on Numberphile: Geobra file relevant to this video: https://www.geogebra.org/m/uPTEQnZs Infinity with James Grime: https://youtu.be/elvOZm0d4H0 Numberphile is supported by

This is one of the top posts on Reddit’s Homework Help. #shorts [Grade 9 Math: Puzzle Involving Toothpicks] byu/allpeoplearebullies 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 you purchase through these links, I may be compensated for purchases

High school geometry is the only super power you need to solve this puzzle! 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

Happy Pi Day! Sato Moshun and Leonardo da Vinci independently devised an incredible visualization to find the formula for a circle’s area. #Shorts (Apologies there was no early access on Patreon–I finished making the video just in time for Pi Day). Wikipedia https://en.wikipedia.org/wiki/Area_of_a_circle#Rearrangement_proof Cut The Knot area of a circle https://www.cut-the-knot.org/Curriculum/Geometry/AreaOfCircle.shtml Area of a circle,

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

Simpsons Book: http://amzn.to/1fKe4Yo — Main Fermat Theorem video: http://youtu.be/qiNcEguuFSA — Water Ballons: http://youtu.be/nacPIOb68Ws More links & stuff in full description below ↓↓↓ Author Simon Singh on Fermat’s Last Theorem in popular culture, especially The Simpsons. Also mentioning Al Jean and David X Cohen. 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

What kind of magic is this?! #shorts 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 ever need to practically convert temperature from weather reports, this is a neat little trick. Just memorize a few values and you can easily convert. I saw this trick in a Lifehacker article. #shorts References https://lifehacker.com/how-to-convert-celsius-to-fahrenheit-without-doing-any-1848777530 https://en.wikipedia.org/wiki/Fahrenheit#/media/File:Thermometer_CF.svg Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not

Complex patterns seen in nature can be generated from relatively simple equations and a golden angle. Song credits Song: Sunflower (Spider-Man: Into the Spider-Verse) Artist: Post Malone, Swae Lee Album: Sunflower References https://en.wikipedia.org/wiki/Fibonacci_number#Nature https://en.wikipedia.org/wiki/Fermat%27s_spiral Fan Wen, CC-BY-SA-4.0 https://commons.wikimedia.org/wiki/File:Helianthus_annuus_-_flower_view_01.jpg Sunflower Javascript code https://www.codeproject.com/Articles/1221341/The-Vogel-Spiral-Phenomenon Sunflower Desmos https://www.desmos.com/calculator/vgh92uz9kl