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[playful instrumental synth music fades slowly]
You know...
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You know...
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Hexagons are the bestagons.
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Why?
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Because bees.
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Bees are the best
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and build only the bestagon, the hexagon.
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Now, I know what you’re thinking.
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Bees build hexagons because they're hexapods
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with hexagon eyes.
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How could they do otherwise?
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Excellent point.
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But the humble bumble has an engineering problem to solve.
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She makes two things: honey and wax.
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The former to eat,
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and the latter to contain the former.
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To make but a little honey,
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she must visit a lot of flowers.
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And to make one unit of wax,
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she needs eight units of honey.
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Wax is costly for bees in flower terms,
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and honey is drippy in food terms,
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so to make a hive that contains the maximum honey
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while using the minimum wax is royally vital.
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Thus, a honeycomb conjecture.
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Which shape works best?
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To answer, we need to talk tiles.
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Tiling is covering a surface with a pattern of polygons.
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There's lots of options
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because there's lots of polygons.
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Even the regulars go on and on-agon.
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Now for bees picking patterns,
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the more complicated ones
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obviously use more lines than necessary.
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That’s what complicated means.
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And thus a honeycomb of that tile
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would use more wax per honey.
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So sticking to the simple regulars,
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there are just three that tile tightly.
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Triangle, square, and hexagon.
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Pentagons are broken hexagons leaving gaps.
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Same with septagons.
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Octagons are alright,
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but they're no hexagon.
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Which leaves the tiling trio which tile differently.
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A square is a square of squares,
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which is a square of squares, and so on.
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Squares tile tidily by basically cheating.
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Covering an infinite plane with an
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infinite number of parallel lines.
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Like, wow, that's what a plane is.
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Boring!
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Triangles pull the same trick,
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dividing themselves down into infinite nothing.
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But not the hexagon!
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The only regular polygon
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to tile a plane without resorting to debasing self-division,
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unlike some squares I could mention.
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At least triangle is trying to be
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more geometrically interesting than square,
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teaming up a bit to…
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one, two, three, four, five, six.
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Wait, hexagon!
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The other shapes can't help it.
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They just want to be the bestagon.
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Even some of the irregulars,
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like rhombus, tile by hexagoning.
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Same with your triakis tilis,
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[with difficulty]
and deltoidal trihexagonals,
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[with continued difficulty]
and your, ah, kisrhombille,
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[with laughter]
and floret pentagonals.
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Look, they're all just hexagons.
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Even Cairo tiles
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(poor pentagons)
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tile up as best they can to form a lumpy hexagon.
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The rest just can't compete with the best.
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The hexagon,
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nobly indivisible,
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is the bestagon.
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Uhh, where were we?
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Oh right, honeycomb conjecture.
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Max honey. Min wax. Three options.
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Okay yes there's the circle.
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A shape defined by the least perimeter for the most area,
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but that only works when you need just one.
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Pack circles and this is the best they can do.
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Look at all that wasted space!
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And even if you pack the gaps,
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you still use more wax.
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And, again, the way these circles,
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arrange themselves …
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it's almost like…
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onetwothreefourfivesix
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hidden hexagon!
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Bees use the hexagon
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because no shape is better to create
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the maximum area for the minimum wall.
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And this min-max stat of hexagon
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is one of the many reason they show up everywhere.
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Including in the aforementioned bee's eyes.
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Each hexagon is a long tube that leads
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to the light-catching cells at the bottom.
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More light equals better vision and
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hexagons let the most light in
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using the least amount of wall.
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So why aren't your eyes hexagons?
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Au contraire mon ami,
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they are l'Hexagone.
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[intensely]
Not on the outside, but on the inside.
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Your light-catching cells are at the back of your eye,
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in a hexagonal grid for the same reason as bees.
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Max light, min wall.
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Your window to the world,
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is but through the hexagon.
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Does that not make it the bestagon?
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Okay, maybe hexagon as min-max-agon
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doesn't catch your fancy.
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Then how about a little mystery, oui?
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Let us travel to Saturn.
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Yes, the rings are attention-grabbing,
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but leave the equator,
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travel north and here lies the unexplained.
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The Great Hexagon of Saturn.
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Need something for scale?
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Well, here's the Earth.
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Oh, here's six the Earths.
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Saturn's hexagon is pretty big.
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What is it?
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Well, you might be thinking it's a geological formation.
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An enormous basalt column
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like the smaller versions you find on Earth.
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But no.
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Saturn is a gas giant.
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There is no surface or geology to speak of.
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So the great hexagon is composed of shapeless clouds
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somehow keeping shape and changing color.
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It's a magnificent solar system mystery.
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And, while I'm no space archeologist,
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if I was looking for an alien-gifted monolith,
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on the most “look at me” planet,
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under a hexagon beacon with earth-sized sides,
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[tongue click]
that's where I would start.
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After all, what aliens would want to make
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first contact with the nearby monkeys
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before they became enlightened
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to pursue the universal truth.
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Hexagon is the bestagon.
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From the largest down to the smallest.
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Say, for example, this tiny snowflake I happen to have,
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that has six sides, as all snowflakes do.
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Gee, what could cause that to be?
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Let's zoom down to the atomic realm and see.
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When water molecules join together to make a flake,
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the sturdy shape they prefer is the hexagon.
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As more molecules join,
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they extend the flake fractally up.
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The beauty of the snowflake on the monkey scale,
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is but an extension of the hexagonal perfection
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on the atomic scale.
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Okay, yes*.*
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You will sometimes find snowflakes with twelve sides,
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but this happens when two growing snowflakes
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get stuck together, so it still counts.
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And the hexagon isn't just for snow,
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but for all ice 1H,
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which means basically all ice on earth.
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Yeah, there's a little ice 1C
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which we don't talk about
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because it's made of cubes,
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and cubes are boring.
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And there's a bit of ice 9.
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No, don't touch that.
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But if there is ice in your drink,
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give thanks to the hexagon for keeping it cool.
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And it's not just water.
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Lots of atoms use hexagons because…
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(take a note)
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hexagons are the bestagons.
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Oh, using a pencil?
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Get ready to have your mind blown
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about the hexagon here too.
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The lead.
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Well, it isn't lead lead, it's carbon.
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And you know what carbon atoms think is the bestagon?
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[snap]
The hexagon.
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Pencil graphite is a whole bunch of hexagonal carbons,
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and when they happen to be in a straight sheet,
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that's graphene,
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which happens to be the strongest
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atomic material in the universe.
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Some of which is in that pencil.
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To tear a sheet of graphene apart,
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you would need a hundred times more force
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than to do so with steel.
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Hexagon is strong-a-gon.
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This is because when hexagons come together,
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they form three-sided joints 120 degrees apart.
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This, for the least material,
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is the most mechanically stable arrangement.
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Pull on one joint,
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and the other two equally pull back,
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push in, and the other two are the
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most able and stable to resist.
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Now look anew at a tiling of hexagons
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and you see it is composed of nothing
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but these max stable joints,
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each arranged perfectly to help the others
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be stronger and stabler.
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This is another reason hexagons show up everywhere.
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The universe blesses stability in her physics,
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from those basalt columns,
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to bubbles which,
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as soon as they can,
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ditch their spheres to become
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as close to hexagonal perfection as they can.
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That's so cool.
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Oh right, yes.
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So if your pencil lead contains
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some of the strongest material in the universe
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how can you write with it?
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Okay, okay.
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This is going to get even more exciting.
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While hexagons are super strong this way,
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they aren't super strong this way.
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On a small scale,
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that means your pencil can break off
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in layers to leave a mark.
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But on a big scale,
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hexagons can be flexible while keeping their strength,
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letting us construct some totally unreal materials.
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Print out a grid of hexagons in whatever,
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from aluminum to cardboard,
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make a little sandwich,
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and pow!
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You've got honeycomb paneling.
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A ridonkulously tear-resistant material
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that's also super light and flexible.
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It's used everywhere
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but particularly in aviation.
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Rockets need to be strong yet light.
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Same for aircraft.
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With wings that really can't tear
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but also need to bend.
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And only the magic of the honeycomb panel
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can do both as well.
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Give thanks to the hexagon for blessing our flight.
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And we still haven't yet discussed
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the most important application of the hexagon.
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Games!
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For centuries there has been great debate over boards,
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squares or hexagons?
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Spoiler... hexagons win.
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Square boards are the first thing
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an unenlightened species would think of.
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They look sensible and are easy to implement,
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but they are terrible,
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ineffective boards that cause spatial suffering.
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On a square board move horizontal
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or vertical one space
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and you've moved one space,
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but move diagonal
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and the distance is the square root of two spaces.
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Gross.
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Diagonals warp the distance pieces move.
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Square boards look even and tidy,
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but it's deceit.
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Their diagonals corrupting the meaning of space and time,
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and of course they must,
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because a square only has four true neighbors.
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Hexagons, however, have six
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which is more than four,
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which is better!
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And the distance from one space to the next
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is the same in every direction.
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One space.
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Just as it should be.
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If you're a game based on squares,
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I'm so sorry.
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But there is hope.
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With thought and effort,
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you can hexagon yourself into a better place.
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As we all should aspire to do,
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spreading order and hexagonal enlightenment
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for, hexagons are the bestagons.
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And now that you agree, with your eyes will see
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their six-sided perfection in all things.
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And you will say to yourself,
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as part of the order
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hexagons are the bestagons.
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Uhh, thanks for stopping by for communicator coffee.
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Now, go. Share the enlightenment of the order with others.
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[click]
