Good evening from formerly, and soon to be, Sunny San Diego!
The question has haunted me for years, and although never fully resolved, deserves an attempt. So here goes.
There are an infinite number of shapes, i personally, like the ones in the 3rd dimension. Within this matrix, there is a limitless potential for a variety of shapes, and among them, only one can be king.
What, then, Is the BEST shape?
Well alot of 3-d shapes are just 2 dimensional ones, but with prism added at the end, like a cylinder, is just a circle prism, basically. Add a third dimension to a rectangle, and you get a rectangular prism, to a triangle, a triangular prism. These are at best faux 3d-shapes.
I’ve eliminated all but almost all of these shapes out of hand, for instance : the best shape is clearly not the rhombus prism....i mean cmon, im not really even entirely sure what it is , but what a dumb name. Something to do with….um , well anyways I’m eliminating all shapes that are just some 2-d shape that added extra of the same same shape, pretending to be a real 3-d shape, posers.
The REAL contenders for Best 3D shape, with a geometric expression if my physique being excluded as clearly unfair, I think aught to be reduced to these following contenders:
(note: suggestions of shapes given unfair consideration are welcomed in the “comments” section)
THE SEMI FINALISTS!
THE CUBE, AKA ( “EL CUBO”)
http://en.wikipedia.org/wiki/Cube_(geometry)
THE SPHERE AKA (“EL ROLLO”)
http://www.phazedance.com/3d/mirroredball.html
http://www.bancodedadosvisual.hpg.ig.com.br/Escher-Hand-With-Reflecting-Sphere.jpg
THE TETRAHEDRON (AKA “EL SHARPO”)
http://indymatrix.tripod.com/polyhedra/models/platonic/tetrahedron.htm
THE DODECAHEDRON (EL COMPLICATO)
(Having fun!)
http://images.google.com/imgres?imgurl=http://www.public.asu.edu/~starlite/images/florida/dodeca32BP.jpg&imgrefurl=http://www.public.asu.edu/~starlite/dodecahedron.html&h=600&w=800&sz=35&tbnid=U3eQmQQhXqoJ:&tbnh=106&tbnw=141&start=18&prev=/images%3Fq%3Ddodecahedron%26hl%3Den%26lr%3D%26sa%3DG
Well, first off, all these shapes are sweet cuz they’re symmetrical in a whole bunch of ways in all three dimensions.
Second, every side on any of these 4 given shapes is exactly the same, and no particular shape has any more than one kind of edge. (yes, the sphere fits these rules, check for yourself.)
Also, all of these shapes are platonic solids, and as much as I despise Plato, and I do, he did pick out some pretty sweet shapes:
http://www.mathacademy.com/pr/prime/articles/platsol/index.asp
A couple rejected Platonic Solids (take THAT Plato!):
The ICOSAHEDRON (see link above) didn’t make the cut, cuz it has 2 different kinds of sides. ICOSAHEDRON , and OCTAHEDRON (see link above) are also platonic solids, but in my opinion, are the runts of the Platonic solid litter. First of, Octahedron uses equilateral triangles which tetrahedron already got dibs on, and did a better job with. Icosahedron, well he did the same thing, and is more round, but will no doubt be knocked out by Dodecahedron, which beats Icosahedron’s ass in both the originality and roundness contests. Not to mention, you could keep throwing triangles together all day to make bigger and bigger spheres,. The tetrahedron is clearly the king of triangle-based 3d shapes, and thus is the only representative thereof. Now, we must take these 4 kings, and determine the true emperor of shapes.
So lets get to the brackets!
Semifinal Round....
First, in the “round or round-ish” division, we have DODECAHEDRON, and SPHERE.
Nobody cares about/ has ever heard of the DODECAHEDRON.
A feature length Hollywood movie about a scary, yet shiny DODECAHEDRON has never been made, unlike the SPHERE. Since the divine or alien “makers” of the SPHERE are clearly more advanced than us, they’d know which was the best shape, and well, Dustin Hoffman didn’t go crazy looking at a giant soccer ball, so sorry DODECA, but yer kerplunked. http://sphere-themovie.warnerbros.com/
Although the most complex, and perhaps cleverest of the shapes, DODECAHEDRON is the nerd of the group, and best serves as advisor, not great leader.
SPHERE beats DODECAHEDRON
Second, in the “don’t drop this on your toe” division, we have, two contestants which have been described as……um… “edgy”……..CUBE and TETRAHEDRON
CUBE, also the namesake of a Hollywood thriller, this rectangular wonder can do a number of amazing things. Unlike all the other shapes in the finals, the CUBE can stack with perfect efficiency. I mean, like perfect, no gaps or nothing. A strong start. http://www.cubethemovie.com/
The TETRAHEDRON, however, may be the progenitor of all the other shapes, as is capable of making a shape with the fewest possible equal sides, and be totally whole. You know what I’m sayin. Also, it is the sharpest. It does not, however, have any practical use for people of any kind. The only things about it that are cool are stuff geometrists care about, and maybe some crystal stuff.
For sheep utility, and amazing mathematical CUBE beats TETRAHEDRON. Maybe tetrahedron should go track down rock and point at his random ugly bumps, and sedimentary layers and shit. He did, after all, make the final four.
THE FINALISTS!
THE GREATEST RIVALS OF ALL THE 3D SHAPES! THE EPIC BATTLE!
CUBE vs. SPHERE
Benefits of the CUBE
1. The cube is composed entirely of right angles, one from each of the three spatial, dimensions at each corner. The very 90 degree angles we use to define these dimensions. Amazing…..orPERHAPS redundant.
2. As mentioned before, nothing stacks like the cube. Unequaled for warehousing, etc.
3. The famously round Epcot center was so freaking weak sauce.
Benefits of the SPHERE
1. The SPHERE has an unparalleled surface area to volume ratio. Best for storing things without stacking.
2. Every point on the surface of a SPHERE is a equal distance from the center. Exactly. No other 3-d shape can do this.
3. The SPHERE is the shape of every star, planet, subatomic particle, major moon, neutron star, black hole, and DEEZ NUTS!
4. SPHERES roll, and like bumbles, often bounce.
5. SPHERE can roll in ANY direction
6. A person traveling along the surface of a SPHERE can visit any point on the surface without ever crossing an edge.
7. The SPHERE may prove to be a more effective way of understanding the spatial matrix, dimensions defined by 90 degree angles could potentially be argued as…..arbitrary.
8. spheres are kind of like boobs, sort of.
9. Epcot center isn’t technically a sphere, it’s a big freakin platonic triangle geodesic thingy.
THE VERDICT!
It seems that, when examined individually, sphere beats cube, but when working in groups, cube is better. But a winner must be chosen, because CUBE is really hanging out in what is truly, sphere’s universe, I gotta go with EL ROLLO.
The best shape is, I hereby declare, to be the SPHERE.
Some additional shapes to ponder:
1.a cylinder extending infinitely in both directions, thus gaining a better surface to volume ratio.
2. since spheres do stack regularly, but with gaps. These gaps, therefore, would be regular as
well, what if we welded something the same shape as the gaps, to the side of a sphere, then maybe it would stack, and keep some pretty good surface area-volume ratios
3. boobs.
anyways......
CONGRATULATIONS SPHERE!
Till Next Time,
Baldacchino.
