General / Off-Topic OCD Pain: Optimal Packing of Squares in Squares

Darren Grey

Darren Grey
CONTENT WARNING: This will make people with any element of OCD cringe. If you additionally have a background in mathematics your eyes will bleed and your brain will melt. Viewer discretion advised.

I present you with... optimal packing of squares in squares:

http://www2.stetson.edu/~efriedma/squinsqu/

This is the mathematically proven least space taken up by x number of squares in a square enclosure. Some fit in very nicely and neatly, but as the numbers get higher the optimal way to pack things becomes messier and messier. Next time you try to stack things in your cupboard in a neat way, remember this and weep.

The lesson here is that the universe hates you. At a base geometrical level we are governed by chaos and disruption and nothing you do can ever fix that. You might as well give up on life now.

Not feeling quite suicidal enough after that? Well, here's a whole page of other shapes in shapes:

http://www2.stetson.edu/~efriedma/packing.html
 

Kerrash

Kerrash
Darren Grey said:
...
The lesson here is that the universe hates you. At a base geometrical level we are governed by chaos and disruption and nothing you do can ever fix that. You might as well give up on life now....[/url]
Click to expand...

AAAARRRGRGHHHH, Must. Reduce. Entropy... :eek:
 

DrBaggy

DrBaggy
Somehow the symmetrical ones are ok but the ones that just look jammed in are just WRONG!

Oh dear, I'm not a mathematician, but look to maths for beauty in a messy world.

As you obviously are a mathematician Darren can I ask you a question? It occurred to me that all the equations I learnt in physics (V=IR, PV=k, f=ma and much more complex ones!) are not the simple sums they purport to be, but all based on statistical averages (and hence all fall apart at the quantum level). So they are more like "1+1= about 2 most of the time, but sometimes a bit more or less, and a lot more if the numbers get small". Is that right or am I getting confused?
 

Darren Grey

Darren Grey
DrBaggy said:
As you obviously are a mathematician Darren can I ask you a question? It occurred to me that all the equations I learnt in physics (V=IR, PV=k, f=ma and much more complex ones!) are not the simple sums they purport to be, but all based on statistical averages (and hence all fall apart at the quantum level). So they are more like "1+1= about 2 most of the time, but sometimes a bit more or less, and a lot more if the numbers get small". Is that right or am I getting confused?
Click to expand...

In some situations yes, at the quantum level this splits apart. A great example of this is the double slit experiment - what path light takes as it goes through a double slit. The light is made of photons, which behaving as photons will go through one slit or the other, shining light on the screen beyond. Ah, but the light is made of waves! and will diffract through the slits, forming a pattern of light and shadow on the screen. Which is right? Well, both. On a quantum level the photons go through a statistical path, going through one or the other, and it's only when you average them out that you see the interference pattern.

However for most real life things you already have that average in place, since there are so many particles involved. So for non-quantum things it's F=ma all the time. The big way real life diverges is that those equations generally assume no friction, air resistance, etc. For an engineer a lot of the physics equations aren't much use.
 

DrBaggy

DrBaggy
Thanks for that speedy reply!!

I love the double slit experiment. That, and Feynman's QED ideas make me realise that the universe is way weirder than anything we can imagine :eek:

Just disappointing physics have given up trying to explain what the equations mean...(they might say there is no higher explanation than the maths?)
 

Darren Grey

Darren Grey
DrBaggy said:
I love the double slit experiment. That, and Feynman's QED ideas make me realise that the universe is way weirder than anything we can imagine :eek:
Click to expand...

It's a marvel that we can imagine anything at all. Our brains were evolved to help a particular type of ape adapt to a few different environments on a small rocky planet in one star system. For us to split the atom, scry the Big Bang, and uncover the fundamentals of how the universe operates is really quite amazing.
 

Sir.Tj

The Moderator who shall not be Blamed....
Volunteer Moderator
Sir.Tj
Darren Grey said:
It's a marvel that we can imagine anything at all. Our brains were evolved to help a particular type of ape adapt to a few different environments on a small rocky planet in one star system. For us to split the atom, scry the Big Bang, and uncover the fundamentals of how the universe operates is really quite amazing.
Click to expand...

“the rest of you... keep banging the rocks together”

― Douglas Adams, The Hitchhiker's Guide to the Galaxy


Say's it all really. :D
 

DrBaggy

DrBaggy
Good point: I guess we're flatlanders trying to explain a 3D universe. And you're right to point the marvels of what we do know. To be able to look back in time through telescopes, for example, or know there are other planets out there, or have find the Higgs boson....things that in my youth would have been thought impossible. I guess we are wired to bank those and peer under the next rock

It's a strong drive though.....

Maybe the mice would know T.J.?
 
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kenwshmt

kenwshmt
https://developer.mozilla.org/en-US/demos/detail/tetris-in-the-browser

Tetris in the browser

By g_marty on Aug 29, 2011

The game interface is fully integrated inside the browser (title & URL bar...)


1314620159_screenshot_1.png
 

Abysinth

Abysinth
Anyone with OCD would know that OCD is wrong.
:eek:
Anyone with OCD would know that the order of the letters are wrong.
:)
Anyone with OCD would know it should be CDO!
:D
 
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Abysinth

Abysinth
Magma said:
You forgot to capitalise one of the letters there. Please correct it; it looks untidy with the rest :p
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Oh the horror, the indignity... :eek:

Your CDO being more pronounced than mine. :eek: :mad:

Corrected... :)

Perhaps you'd correct your post too, then my misteak(sic) would be hidden for all time...
 
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