The Infinite Pattern That Never Repeats

a portion of this video was sponsored by lastpass this video is about a pattern people thought was impossible and a material that wasn't supposed to exist the story begins over 400 years ago in prague i'm now in prague and the czech republic which is perhaps my favorite european city that i've visited so far i'm going to visit the kepler museum because he's one of the most famous scientists who lived and worked around prague i want to tell you five things about johannes kepler that are essential to our story number one kepler is most famous for figuring out that the shapes of planetary orbits are ellipses but before he came to this realization he invented a model of the solar system in which the planets were on nested spheres separated by the platonic solids what are the platonic solids well they are objects where all of the faces are identical and all of the vertices are identical which means you can rotate them through some angle and they look the same as they did before so the cube is an obvious example then you also have the tetrahedron the octahedron the dodecahedron which has 12 pentagonal sides and the icosahedron which has 20 sides and that's it there are just five platonic solids which was convenient for kepler because in his day they only knew about six planets so this allowed him to put a unique platonic solid between each of the planetary spheres essentially he used them as spacers he carefully selected the order of the so that the distances between planets would match astronomical observations as closely as possible he had this deep abiding belief that there was some geometric regularity in the universe and of course there is just not this two kepler's attraction to geometry extended to more practical questions like how do you stack cannonballs so they take up the least space on a ship's deck by 1611 kepler had an answer hexagonal close packing and the face centered cubic arrangement are both equivalently and optimally efficient with cannonballs occupying about 74 percent of the volume they take up now this might seem like the obvious way to stack spheres i mean it is the way that oranges are stacked in the supermarket but kepler hadn't proved it he just stated it as fact which is why this became known as ...