The perfect Display

I imagine this display might be possible someday. There are three main things you do with LCD screens, viewing content abstractly related to looking at a piece of paper, tasks related to producing those or using other programs and watching movies. Here are the relevant aspect ratios:

So you see on the top left is the typical U.S. paper size 11x8.5, but I left enough space around it to handle the standard the rest of the world uses A4... But in some bizarre mathematical coincidence A4 is the perfect size to fit a U.S. standard size into and have room for all the toolbars and scroll bars and everything.
   The HDTV's now are 1.77:1 aspect ratio. But the movies you see in the theater are 2.39:1, A4 is 1.414:1 so two longways is 2.8:1.  So the idea is you would have two screens the A4 size, that you could put side by side so you can work on two different things full size but then you rotate both of them and put them side by side to go into movie mode. Unfortunately there are still black bars around the movie but this is the best I could do. And Hollywood historically has always gone to wider and wider screen 2.39:1 is the current that I used above.
  The big technical hurdle is making an lcd without a bezel, I found one 40 inch HDTV that the bezel was only four pixels wide (which would still be annoying going down the middle of the display) but that TV was 5000 dollars so right now it is expensive to do but hopefully this will be possible someday...
   I call the screens "Foils" so someone can say "Lock Foils into Movie position!"

***UPDATE***
A friend of mine, Blair Updike, suggested using projectors instead. The image projected doesn't have the limitation of the bezel around the lcd and I believe that makes it possible a lot sooner than what I had in mind. The projector would basically be two projectors built in one case that can rotate and move what they are projecting from one mode to the other.

gclamps

These are supposed to lock tight like the mechanism on the gas pump.

a natural number size kite

consider the type of number 3^(1/4)*2*y = x for natural number y.
When you plug x in for all 3 sides of Heron's formula you get:

and then fill in for x:

So this type of number makes an equilateral triangle have a natural number area. 

Interestingly because of the 3 in 3y^2, that means:

This shape I believe is called a kite, because it is 1/3 of the triangle's area it will have an area of y^2. So it has the same area as a perfect square but a different shape. 

This hexagon has area 6*y^2. 

which is the same as the surface area of this cube:

If you imagine this tiling of hexagons made to look like cubes:

You can see layers of hexagonal tiling would be able to map the surfaces of a volume of cubes in a way that preserves area. Though not shape.