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Annoying Carpet
https://gladerebooted.net/viewtopic.php?f=7&t=10457		 Page 1 of 1
Author:  Arathain Kelvar [ Thu Oct 03, 2013 7:40 am ]
Post subject:  Annoying Carpet
Ok, first I must preface this with I AM NOT OCD. I swear.

Moving on...

The carpet in our office is made up of square carpet "tiles". Each as a quarter circle design:

Image

The circle is subtle, and beneath the design on the carpet itself. But, you can see it.

Now, the tiles are placed with random (seemingly) orientation. Therefore, one can expect in any group of 4 tiles, there is a small chance that a circle is formed, an equal chance that a curvy "+" sign is formed, and a great chance that some other dismissible pattern is formed.

So first, when walking around the office, I immediately notice when there's a circle. So much so that I have thus far found 5 circles and I remember where they are. So there's that.

Secondly, I find myself wanting to calculate the odds of a circle, and thereby extrapolate to predict how many circles are in the building. However, it's not as easy as you might thing. While you could quickly calculate how often an isolated group of 4 tiles would make a circle, the building is not made up of isolated groups of 4 tiles. Each tile that fails to contribute to a specific group of 4's circle is necessarily contributing to another group.

This is solvable, but I refuse to pick up a pencil and a calculator, because, well, that would be OCD - and as I said I'm not OCD. Instead, I am left to try and figure this out in my head as I walk around the office (this is the non-OCD alternative), which I have not devoted enough energy to being able to do.

So, instead, it's just distracting and annoying.
Author:  Arathain Kelvar [ Thu Oct 03, 2013 7:58 am ]
Post subject:  Re: Annoying Carpet
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Attachments:
circles.jpg
circles.jpg [ 74.21 KiB | Viewed 4248 times ]
Author:  Kaffis Mark V [ Thu Oct 03, 2013 8:16 am ]
Post subject: 
Choose an arbitrary tile. That tile will contribute to one block's circle, if the appropriately chosen other 3 tiles are also oriented in the correct 1 direction out of 4 possible directions.

(1/4)^3, then, no? 1/128

This doesn't account for disruptions in the probability caused by edges of the tile space, etc.
Author:  shuyung [ Thu Oct 03, 2013 9:48 am ]
Post subject: 
You could probably formulate a query on WolframAlpha that would tell you.
Author:  Arathain Kelvar [ Thu Oct 03, 2013 10:11 am ]
Post subject: 
LOL I mentioned this to my father. His response:

This is easily solvable without mathematics. Every time you find a circle, spill coffee on it. Over time, these tiles will be replaced, assumably with a random pattern. The number of circles in the building will converge on zero.
Author:  Taskiss [ Thu Oct 03, 2013 5:49 pm ]
Post subject:  Re:
Kaffis Mark V wrote:
Choose an arbitrary tile. That tile will contribute to one block's circle, if the appropriately chosen other 3 tiles are also oriented in the correct 1 direction out of 4 possible directions.

(1/4)^3, then, no? 1/128

This doesn't account for disruptions in the probability caused by edges of the tile space, etc.

Wouldn't the number of possible combinations of 4) 4 sided objects be 4^4, and since only 1 confirms to a circle ... 1 out of 256?

Then, you'd need to know the number of instances in the room where there are 4 adjacent tiles...and that depends on the room.
Author:  Kaffis Mark V [ Thu Oct 03, 2013 6:01 pm ]
Post subject:  Re: Re:
Taskiss wrote:
Kaffis Mark V wrote:
Choose an arbitrary tile. That tile will contribute to one block's circle, if the appropriately chosen other 3 tiles are also oriented in the correct 1 direction out of 4 possible directions.

(1/4)^3, then, no? 1/128

This doesn't account for disruptions in the probability caused by edges of the tile space, etc.

Wouldn't the number of possible combinations of 4) 4 sided objects be 4^4, and since only 1 confirms to a circle ... 1 out of 256?

Then, you'd need to know the number of instances in the room where there are 4 adjacent tiles...and that depends on the room.

You're calculating the probability of a given 4-tile square containing a circle.

I'm calculating the probability that a given tile will be part of a circle.

I don't need to calculate the size of the room -- I've calculated for an infinitely tiled plane, and stated that I'm not accounting for boundaries. ;)

It's like that old joke among physicists.. "Assuming a spherical cow..."
Author:  Arathain Kelvar [ Fri Oct 04, 2013 6:31 am ]
Post subject:  Re: Re:
Taskiss wrote:
Kaffis Mark V wrote:
Choose an arbitrary tile. That tile will contribute to one block's circle, if the appropriately chosen other 3 tiles are also oriented in the correct 1 direction out of 4 possible directions.

(1/4)^3, then, no? 1/128

This doesn't account for disruptions in the probability caused by edges of the tile space, etc.

Wouldn't the number of possible combinations of 4) 4 sided objects be 4^4, and since only 1 confirms to a circle ... 1 out of 256?

Then, you'd need to know the number of instances in the room where there are 4 adjacent tiles...and that depends on the room.


Right, but each 4x4 group that fails to form a circle increases the odds of a circle being formed adjacent, since at least one quarter circle must be turned away and toward the next potential group. And thus, the two groups in question overlap.
Author:  Arathain Kelvar [ Fri Oct 04, 2013 6:38 am ]
Post subject:  Re:
Kaffis Mark V wrote:
Choose an arbitrary tile. That tile will contribute to one block's circle, if the appropriately chosen other 3 tiles are also oriented in the correct 1 direction out of 4 possible directions.

(1/4)^3, then, no? 1/128

This doesn't account for disruptions in the probability caused by edges of the tile space, etc.


I'm not following you with this. I get the premise, but what's with the then, no?
Author:  Kaffis Mark V [ Fri Oct 04, 2013 7:45 am ]
Post subject: 
The "then, no?" is a negatively framed question format. Why did I choose that? I have no idea.
Author:  Corolinth [ Fri Oct 04, 2013 8:07 am ]
Post subject: 
It is more OCD to go on about how you're not OCD enough to get out a pencil and paper and work out the problem while you wander around being distracted and irritated by the problem than it would be to actually do the math.
Author:  Arathain Kelvar [ Fri Oct 04, 2013 9:50 am ]
Post subject:  Re:
Corolinth wrote:
It is more OCD to go on about how you're not OCD enough to get out a pencil and paper and work out the problem while you wander around being distracted and irritated by the problem than it would be to actually do the math.


Someone needs to purchase a sense of humor.
Author:  Stathol [ Fri Oct 04, 2013 9:52 am ]
Post subject: 
I'm sorry, but I have to do this to you:

http://www.reddit.com/r/mildlyinfuriating
http://www.reddit.com/r/mildlyinteresting
Author:  Arathain Kelvar [ Fri Oct 04, 2013 10:32 am ]
Post subject:  Re:
Stathol wrote:
I'm sorry, but I have to do this to you:

http://www.reddit.com/r/mildlyinfuriating
http://www.reddit.com/r/mildlyinteresting


OMG NO!!!!

Image
Author:  Kaffis Mark V [ Fri Oct 04, 2013 12:44 pm ]
Post subject: 
Some carpet layer really hates bishops.
Author:  Corolinth [ Fri Oct 04, 2013 5:16 pm ]
Post subject: 
At least, he hates the black bishop.
Author:  Kaffis Mark V [ Fri Oct 04, 2013 7:44 pm ]
Post subject:  Re:
Corolinth wrote:
At least, he hates the black bishop.

Racism!
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