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Booooo

I am deeply conflicted, and believe that the best way to interpret my indecision is to conclude that I love all polygons equally.

@IsaacKing Outrageous but understandable

We put in a good fight team NO :)

The argument about encoding arbitrary information was compelling, but then I realized that hexagons can do that too by varying their side length.

@IsaacKing I thought of that later but chose not to bring it up. Glad to hear you thought of it, too

@IsaacKing resolve please?

@IsaacKing Did you believe that hexagons were the bestagons when the market closed?

Hexagons are beautiful, robust and one of natures most exciting shapes. But the triangle is by far the bestagon.

Not only is a hexagon just a beautiful arrangement of triangles, but in 3D computer graphics for example, almost everything is made out of triangles.

Triangles gave us trigonometry, the pyramids, pizza slices, ramps and the pointy end of an arrow.

Want to explain the geometry of a non-euclidian space in an easy way?

Tell them a triangle doesn't have 180⁰ there.

Want to find the area of another polygon? Make it triangles.

Want to spice up your orchestra performance with a little cutesy sound?

You guessed it, Triangle.

The most recognizeable and stable shape, the first collection of connected points that turns one dimension into two - the triangle has it all.

So yes, Hexagons are good. But at their heart beats an ancient core. Pythagoras' last gift to humanity:

The Triagon,

truly the Bestagon

I read through the comments but I still feel like I don't have enough information. Of the arguments you've been exposed to for the various polygons so far, which arguments have resonated with you, or by how much?

All right, stop. No one place any more bets. Resolve the market. We're at 66%...done.

@PatrickDelaney Resolve the market at 66% with a 66% chance estimated by the market. Perfect. Number.

Given that CGP Grey has just joined Manifold, and they're known to have some strong opinions about hexagons, would anyone object to me lengthening this market to give them and their fans a chance to weigh in?

Oh wait, they already have.

@IsaacKing You could extend it to the 6th!

@PatrickDelaney Or even 6/6!

Six is the first perfect number in the decimal system, so by definition no other -agon can ever be more perfect. To see how insane perfect numbers are, read here: https://mathworld.wolfram.com/PerfectNumber.html 6 is ALSO the third triangular number after 1 and 3, and honestly it's really not that impressive that 3 is a triangular number, and 1 has so many special properties, that's kind of a default, so 6 is also the best triangular number. Tiling using regular polygons has been talked about already and dismissed but that dismissal has failed to point out the fact that the interior angles of hexagons are 120 degrees, which divides evenly into 360, the only other polygon this works for is the Pentagon, which...is 5 not a perfect number. For anyone who is religiously Jewish, the interior of the Star of David is a Hexgon, so you kind of have to vote yes, or at least consult a Rabbi if not. If you're antisemetic, fuck you, get off of this market. Using Pascal's triangle, if you put a hexagon around any number, the opposite sides groups will point toward numbers, the product of which will always result in 600. Finally, snowflakes are always six-sided because of the efficient packing of hexagonal shapes, which is a funny contrary to think about in response to, "you're a special snowflake," because snowflakes are in actuality all extremely similar to one another given their hexagonal nature.

@PatrickDelaney And why do snowflakes generally have this six-way symmetry? It’s because that’s an emergent property of combining the underlying tetrahedral water molecules. Tetrahedra are composed of triangles, the ultimate building block.

@JimHays Johannes Kepler used cannon balls to explain it: http://www.joostwitte.nl/M_Galilei/Johannes_kepler_snowflake.pdf Nasa used youtube: https://www.youtube.com/watch?v=jbgpVE6sTpE

@CGPGrey W

Social pressure for YES just went way up

Updating my position upon considering new-to-me information about how great Triangles are

Hexagons being the bestagon is pure I-want-to-feel-clever contrarianism.
The CGP Grey video cherrypicks the few specific things hexagons are best at to do its comparisons.

There's a reason we don't live in hexagonal buildings on hexagonal city blocks and use graph paper instead of hexagon-tile paper. In fact, there's lots of reasons.

If you live by the beach you find the view less beautiful than someone who's visiting. I don't think this is contrarianism, just human nature.

Just realized this number is meaningless without a base rate.