June 25, 2012 - A Penny for your Thoughts

[SIZE="2"]From Floor and Decor.

Here's another image showing it being laid out.[/SIZE]

Find a penny pick it up...

This might take a while.

It's common cents.

Oh, yeah: Thanks classicman.

I couldn't get your original image to copy as an image. It says it's a part of a video.

no prob.. here ya go.

Hey Kerosene - Does that father in the pic look like anyone you know?

Probably not to you, but I did a double-take when I first saw it on my news feed.

Another fun fact, math nerds please verify....
I read that the cost per sq ft. was $2.58 in pennies.
GO!

The diameter of a US penny is 0.750 inches, so it's area is 0.4415 sq in.
A 1x1 ft square has an area of 144 sq in.

The pattern for maximum packing of US pennies in a 1x1 ft square
is left as a simple mind-exercise for the Reader... :rolleyes:










Mathematics

Is there a simple equation that can be used to show how many circles of radius (r)
can be packed into the rectangle (l x w), in the optimal way? So that no circles overlap.
(r is less than both l and w).

...And it seems the answer is "we don't really know" :)

I would ask why you insist on packing a square foot of pennies in a shape that is a square? To my mind, a square foot of pennies could be much more reasonably accommodated in a hexagon.

because your parents were honeybees ?

because circles pack well in hexagons

Maybe he grew up in Hex House.

Oh, bee hive!

Squashing my buzz. :mad:

I want a DIY guide. How do you seal those down? We have wood laminate floors now, could you do it on top of that?

http://cellar.org/iotd.php?threadid=20604

and I'll raise

http://cellar.org/iotd.php?threadid=23711

For blueboy in D-Jim's link from 2009 ... better late than never

I have a few wheat pennies. I love wheat pennies and separate them whenever I see one. But not nearly enough for a cool project like that! Then again, you kind of want to see the front and back of wheat pennies.

BigV;817014 wrote:

because circles pack well in hexagons

V, I was trying to be facetious... :rolleyes:

I agree a single circle packs very efficiently in a single hexagon.
But unless the floor is a hexagon of exactly the right size for US pennies,
the problem changes to one of optimal packing hexagons.

I assumed a regular shape of a rectangle or square.

Erich's packing center
Packing Equal Copies
[ATTACH]39268[/ATTACH]

Unit circles in a square
[ATTACH]39270[/ATTACH]

Unit circles in a hexagon
[ATTACH]39269[/ATTACH]

So without changing the size and/or shape of the floor to accomodate the US penny,
the optimal packing pattern may more difficult/impossible to find.

You are going to be right against two walls and within the diameter of a penny from the other two. Thats what trim is for.
So back to my original question how many pennies fit in a 12"x12" space?

classicman;817054 wrote:

You are going to be right against two walls and within the diameter of a penny from the other two. Thats what trim is for.
So back to my original question how many pennies fit in a 12"x12" space?

Technically, I think you have changed the problem, but...
The simplest pattern to visualize is this:

[ATTACH]39274[/ATTACH]

If pennies are 0.75 inches in diameter, this pattern would hold 16 per linear foot.
16 x 16 = 256, or $2.56/sq ft.

But the pattern used in the OP was different, and more efficient.
So if you change the pattern towards a more "optimum" packing,
(or towards maximum number that will fit in a square foot)
the number or cost, obviously, would be higher.

The difficulty in calculating the optimum packing comes in selecting repeating "tiles" that fit the specific area efficiently.
Just as BigV said earlier. Circles fit hexagons very efficiently, but hexagons don't fit squares efficiently at the edges.

so the figure I read was relatively accurate. thanks.
I believe that amount would give one a good idea of the cost to cover their floor
... within a few pennies anyway.

•Some sources indicate that the amount of pennies, but of course it might vary. One source said it took about $7.50 in pennies per square foot. So that’s quite a lot of pennies, but is still cheaper than making a customized flooring professionally. But of course it depends of the size of your floor, and your penny spacing.

From mah link up thar. Don't know how it's relevant or not relevant 'cause I barely read a damn word any of ya said about cost and pennies per square foot. :lol:

lol - thats what made me post my original question. :p:
I think that number actually refers to the TOTAL cost per sq ft, but was written incorrectly.

classicman;816985 wrote:

Hey Kerosene - Does that father in the pic look like anyone you know?

Probably not to you, but I did a double-take when I first saw it on my news feed.

Hmm...a little like my husband, I suppose lol...I wish he was make me a floor like that!

:)
Actually now that I saw some more pics of him on FB - not as much as I thought. :/