What is the area of a ring (an annulus), the region between two concentric circles? The line segment is tangent to the inner circle and has a length of 8. The answer is surprising and there are several ways to solve the problem. In the video I present four solution methods and also mention a fifth method that is an introduction to visual calculus. *I posted this 3 months before Vsauce's napkin ring video, so it's interesting to see Vsauce did the 3d version of this problem to huge popularity. Link to Vsauce video: https://www.youtube.com/watch?v=J51ncHP_BrY Desmos interactive https://www.desmos.com/calculator/siqwbkbmkn My blog post for this video (sources and links for further exploration) https://wp.me/p6aMk-5cZ Thanks to all patrons! Special thanks to: Marlon Forbes Shrihari Puranik Kyle 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 whichever method is most convenient for you. My Blog: http://mindyourdecisions.com/blog/ Twitter: http://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Google+: https://plus.google.com/108336608566588374147/posts Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: http://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: http://www.patreon.com/mindyourdecisions Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.9/5 stars on 29 reviews) https://www.amazon.com/gp/product/1500497444 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 2 reviews) https://www.amazon.com/gp/product/1523231467/ "Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews. https://www.amazon.com/gp/product/1517421624/ "Math Puzzles Volume 2" is a sequel book with more great problems. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/1517531624/ "Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 4 reviews) https://www.amazon.com/gp/product/1517596351/ "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews) https://www.amazon.com/gp/product/1517319307/ "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews) https://www.amazon.com/gp/product/150779651X/ "Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/1500866148/