Check out our Patreon page- https-//www.patreon.com/teded View full lesson- http-//ed.ted.com/lessons/why-don-t-perpetual-motion-machines-ever-work-netta-schramm Perpetual motion machines -- devices that can do work indefinitely without any external energy source -- have captured many inventors' imaginations because they could totally transform our relationship with energy. There's just one problem- they don't work. Why not? Netta Schramm describes the pitfalls of perpetual motion machines. Lesson by Netta Schramm, animation by TED-Ed.

Sign up for our newsletter and never miss an animation- http-//bit.ly/TEDEdNewsletter View full lesson- http-//ed.ted.com/lessons/the-infinite-hotel-paradox-jeff-dekofsky Want more? Try to solve the buried treasure riddle- https-//www.youtube.com/watch?v=tCeklW2e6_E The Infinite Hotel, a thought experiment created by German mathematician David Hilbert, is a hotel with an infinite number of rooms. Easy to comprehend, right? Wrong. What if it's completely booked but one person wants to check in? What about 40? Or an infinitely full bus of people? Jeff Dekofsky solves these heady lodging issues using Hilbert's paradox. Lesson by Jeff Dekofsky, animation by The Moving Company Animation Studio.

Check out our Patreon page- https-//www.patreon.com/teded Can folding a piece of paper 45 times get you to the moon? By seeing what happens when folding just one piece of paper, we see the unbelievable potential of exponential growth. This lesson will leave you wanting to grab a piece of paper to see how many times you can fold it! Lesson by Adrian Paenza, animation by TED-Ed.

Check out our Patreon page- https-//www.patreon.com/teded View full lesson- https-//ed.ted.com/lessons/a-brief-history-of-banned-numbers-alessandra-king They say the pen is mightier than the sword, and authorities have often agreed. From outlawed religious tracts and revolutionary manifestos to censored and burned books, we know the potential power of words to overturn the social order. But as strange as it may seem, some numbers have also been considered dangerous enough to ban. Alessandra King details the history behind illegal numbers. Lesson by Alessandra King, directed by Juan M. Urbina Studios. Thank you so much to our patrons for your support! Without you this video would not be possible. Yankai Liu, Ghassan Alhazzaa, Milos Stevanovic, Narat Suchartsunthorn, Joy Love Om, Gi Nam Lee, Shawn Quichocho, Simone Kidner, Dale Dualan, Barun Padhy, Sarah Ford, Jessica James, John Ess, Brandy Jones, Devin Harris, Tony Trapuzzano, Stephen Michael Alvarez, Tom Lee, Juliana, Jason Weinstein, Hoang Ton, Kris Siverhus.

Check out our Patreon page- https-//www.patreon.com/teded View full lesson here- http-//ed.ted.com/lessons/the-mathematics-of-sidewalk-illusions-fumiko-futamura Have you ever come across an oddly stretched image on the sidewalk, only to find that it looks remarkably realistic if you stand in exactly the right spot? These sidewalk illusions employ a technique called anamorphosis -- a special case of perspective art where artists represent 3D views on 2D surfaces. So how is it done? Fumiko Futamura traces the history and mathematics of perspective. Lesson by Fumiko Futamura, animation by TED-Ed.

View full lesson- http-//ed.ted.com/lessons/what-is-zeno-s-dichotomy-paradox-colm-kelleher Can you ever travel from one place to another? Ancient Greek philosopher Zeno of Elea gave a convincing argument that all motion is impossible - but where's the flaw in his logic? Colm Kelleher illustrates how to resolve Zeno's Dichotomy Paradox. Lesson by Colm Kelleher, animation by Buzzco Associates, inc.

Check out our Patreon page- https-//www.patreon.com/teded View full lesson- http-//ed.ted.com/lessons/the-unexpected-math-behind-van-gogh-s-starry-night-natalya-st-clair Physicist Werner Heisenberg said, "When I meet God, I am going to ask him two questions- why relativity? And why turbulence? I really believe he will have an answer for the first." As difficult as turbulence is to understand mathematically, we can use art to depict the way it looks. Natalya St. Clair illustrates how Van Gogh captured this deep mystery of movement, fluid and light in his work. Lesson by Natalya St. Clair, animation by Avi Ofer.

View full lesson- http-//ed.ted.com/lessons/how-big-is-infinity Using the fundamentals of set theory, explore the mind-bending concept of the "infinity of infinities" -- and how it led mathematicians to conclude that math itself contains unanswerable questions. Lesson by Dennis Wildfogel, animation by Augenblick Studios.

View full lesson- http-//ed.ted.com/lessons/exploring-other-dimensions-alex-rosenthal-and-george-zaidan Imagine a two-dimensional world -- you, your friends, everything is 2D. In his 1884 novella, Edwin Abbott invented this world and called it Flatland. Alex Rosenthal and George Zaidan take the premise of Flatland one dimension further, imploring us to consider how we would see dimensions different from our own and why the exploration just may be worth it. Lesson by Alex Rosenthal and George Zaidan, animation by Cale Oglesby.

View full lesson on ed.ted.com- http-//ed.ted.com/lessons/why-do-airlines-sell-too-many-tickets-nina-klietsch Have you ever sat in a doctor's office for hours, despite having an appointment? Has a hotel turned down your reservation because it's full? Have you been bumped off a flight that you paid for? These are all symptoms of overbooking, a practice where businesses sell or book more than their capacity. So why do they do it? Nina Klietsch explains the math behind this frustrating practice. Lesson by Nina Klietsch, animation by Anton Trofimov.

View full lesson- http-//ed.ted.com/lessons/football-physics-the-impossible-free-kick-erez-garty In 1997, Brazilian football player Roberto Carlos set up for a 35 meter free kick with no direct line to the goal. Carlos's shot sent the ball flying wide of the players, but just before going out of bounds it hooked to the left and soared into the net. How did he do it? Erez Garty describes the physics behind one of the most magnificent goals in the history of football. Lesson by Erez Garty, animation by TOGETHER.

View full lesson- http-//ed.ted.com/lessons/the-case-of-the-missing-fractals-alex-rosenthal-and-george-zaidan A bump on the head, a mysterious femme fatale and a strange encounter on a windswept peak all add up to a heck of a night for Manny Brot, Private Eye. Watch as he tries his hand at saving the dame and getting the cash! Shudder at the mind-bending geometric riddles! Thrill to the stunning solution of The Case of the Missing Fractals. Lesson by Alex Rosenthal and George Zaidan, animation by TED-Ed.