Cookie jar math
[29 Mar 2010]
Kuih bangkit is an Asian (more specifically, Nyonya) sweet made from flour, coconut milk, egg, sugar and vegetable oil.
I was struck by how neatly the cookies were arranged in the red-topped plastic container. (These are ubiquitous in SE Asia.)
There are 10 pieces in each outer row.
There is some interesting mathematics behind neat packaging, called tessellation.
We know that bees are quite mathematically clever. Their honeycombs use a hexagon shape since it gives them the largest possible space with least amount of wax, while also being able to pack them together with no dead space remaining. This is called tessellating.
Tessellations is an important area of mathematics and has wide applications in the packaging industry, as well as in tiling and carpets.
Back to the Cookie Container
So how did the kuih bangkit bakers decide on the best size for their cookies?
Either they ordered the plastic containers to suit or they made the cookies the correct size to fit existing containers. Let’s assume it’s the latter (for the purposes of this mathematical discussion).
The container is 10.5 cm across, so its circumference is
10.5 × π = 33.0 cm.
The simple solution would be to make each cookie 3.3 cm across (so we can fit 10 around the edge), but that wouldn’t work. Each cookie is 1 cm thick, and we need to allow for that.
The inner diameter of the cookies will be 2 cm less than the outer diameter (1 cm on each side).
The inner circumference will be
8.5 × π = 26.7 cm
So we need to make the cookies 2.7 cm across.
The inner radius is 8.5 cm and the outer radius is 10.5 cm. The above image is drawn to scale. You can see that a width of 2.7 cm works.
Indeed the cookies are 2.7 cm wide:
See more on Tessellations.