Super Egg - Numberphile

Key Takeaways

what I've got here I have got a super egg this is from the 1970s in this wonderful Leather Pouch that you know is very very Game of Thrones and out it pops even though it's an egg it's an egg that stays up absolutely beautiful yeah and it's a mathematical object and the history of this object is fascinating it's a great story and it's also lead to some really quite good fun maths so why don't I tell you the story it all starts with Swedish Town planners and Swedish Town planners circle's Tor is a square well it's actually not Square this is the problem it was a rectangle in the middle of Stockholm and they wanted to put a roundabout in it okay if they were going to put a circle you know you're wasting this space no Circle if you put an ellipse this is an ellipse here it's too narrow the traffic is going to get squashed couldn't do an ellipse so they were thinking about what shapes they could use and they end up asking this Danish guy he was actually a poet and a mathematician like an amazing renaissance man called Pete Hine and Pete Hine came up with a solution and the solution was something called a super ellipse I'm going to just start with the equation for a circle x^2 + y^2 = 1 okay if this this is one this is a circle let's play around with this but let's enlarge the exponent so let's go to x say to the four plus y four equals 1 what this turns into and these are actually called lame curves is that it gets a little bit fatter gets a little bit fatter okay it's like it's becoming a square so if we did the square this is the square it's becoming a little bit towards it so and I apologize for my rubbish writing let's go to x to 8 + y 8 = 1 this looks basically looks like you know a baby Bell cheese stuck in a box if we were to go to say x to the infinity + y the infinity = 1 it would be the square okay so by playing around with the exponent it sort of Puffs out and get approaches uh in the limit the square squaring Circle exactly you could call it a squirkle let's now start with an ellipse this is a really rubbish ellipse the equation for this is X uh over 3 squar + y / 2^ 2 = 1 and let's do exactly the same thing if we were to turn this to a four it gets a bit chunkier if we were to then turn it to an eight it would get even it would be almost looking like the rectangle so what Pete Hine who had to try and find a shape for the traffic to go around in serle's talk is that he started so just say here this is the um aerial view of cirle Tor and he started with the ellipse which as I said before could do an ellipse it's too narrow here and he actually increased the exponent to get what he called a super ellipse so the super ellipse is halfway in between the actual ellipse and the rectangle and the exponent that he felt was both the most aesthetic and the most practical was 2.5 and it is true that this was then implemented and circle's T which is it's got this kind of horrible kind of Obelisk thing in the Cent at the moment it's bright in the center of Stockholm but more than that this shape it became an icon of 1970s design and the azteka stadium where uh the final of the World Cup was held you look at the roof the AA Stadium that's a super ellipse and there's loads of other Danish design that Ed this shape and what Pete Hine discovered was that if he was going to make his super ellipse three-dimensional it looked like this and actually it was an ellipse because obvious an ellipse would just fall over it's got a peak the super ellipse um actually stands lame a French mathematician also did work on this sometimes they're called lame curves but now because Pete Hine so famous they would be called superellipses this number file video is made possible by the mathematical Sciences Research Institute but we'd also like to thank a special sponsor for this video audible.com they are the leading provider of of audio books and other spoken word Publications they have loads of stuff on their website it's seemingly endless and among them is actually the book Alex's adventures in numberland by Alex Bellos who is the person you just watched in this video and one of the best things about this audio book is not only is it a brilliant best-selling book but it's read by Alex himself so you can hear him tell you all about it entering the world of maths as an adult was very different from entering it as a child and yes there is a whole bunch of stuff about super ellipses in this book and if you want to look for some other mathematical reading well there's loads of stuff on Audible so go to audible.com in fact if you go to audible.com/numberphile they'll know you came from here and you can also sign up for their 30-day trial which lets you download a free audio book and you could make it Alex's inventures in numberland if you want or one of the countless other ones they have available thanks to Audible for their support of this video but