Ryan McGuire wrote:If I recall, a penny is 19mm in diameter, and they appear to be packing them like hexagons.
Henry Wong wrote:
Regardless, how does the math work to get to $2.97 per square feet? It obviously isn't $1.44, which I am thinking was calculated assuming pennies that are one-inch diameter, in a square pattern (which clearly, they are not).
Ryan McGuire wrote:
* As luck would have it, I remember from high school the formula for the area of a hexagon given its side-to-side diameter, but I still have to work it out when give the length of one side. A = D^2 * sqrt(3)/2
Henry Wong wrote:BTW, I never knew the formula for a hexagon. I had to calculate it as six equilateral triangles, where the height is the radius of the penny, and the base is calculated via trigonometry (of a 30/60/90 triangle).
Amit Ghorpade wrote:If it were per square foot, then how does it matter if it is arranged as a hexagon? I admit that geometry was not my cup of tea ever, but still.
So I calculated using the total mm in a square foot given by fred which is 92,903.04 mm and dividing it by area of the penny which is 285.022 square mm.
Which gives me $3.26. Am I missing something obvious here??
fred rosenberger wrote:in other words...
A penny is a circle. you cannot get solid coverage with circles, as there are spaces between them.
You can with hexagons, or squares, or many other shapes...
Take a look at this. You can see some shpaes allow complete coverage with no overlaps or gaps, and others don't. There are also better ways to 'pack' them in. If you aligned them in a square grid, you'd have larger gaps than if you off-set each row - you can kind of squeeze down the size of the gaps. I believe that packing them this way minimizes the gaps, and is best represented by a hexagon.
Ryan McGuire wrote:Square grid -> larger gaps -> fewer pennies -> cheaper per square foot.
fred rosenberger wrote:iA penny is a circle. you cannot get solid coverage with circles, as there are spaces between them.
Matthew Brown wrote:But you would have to factor in greater wear-and-tear on your shoes.