# Real Mathematics – Geometry #14

Mathematics in Bazaars

Some of the vivid memories I’ve got from my childhood consist of absurd bazaar adventures. I am the youngest of three brothers and that brought obligatory assignments with it. Going to bazaar and helping my parents was a key one. Every Sunday a bazaar was set up in our neighborhood. This is the only reason why I dislike Sundays. Monday syndrome? I adore Mondays!

I can count tens of reasons why I dislike bazaars so much. But there was (and still is) something which makes bazaar shopping bearable for me: Fruit & vegetable stands.

Since I was a little boy, I admired the geometrical shapes that are being used in the fruit & vegetable stands. I must confess something: When I was a child I thought there was a law for bazaar workers; they had to align the fruits & vegetables in certain ways. Later on I found out that there was such law and it was in fact a law of mathematics/nature.

Different Packaging

Inside the geometrical festive of bazaars there was a shape which bothered me; Egg case. Fruits and vegetables arrive to the bazaars in cases like the following:

For some reason egg cases opposed to the traditional geometrical agreement of the bazaar:

Why do eggs align differently? Was I the only one who realized this fact?!

I’ve Got Oreos

Let’s say that you are drinking coffee in a Starbucks and enjoying a big box of oreos. Suddenly you realize the boy/girl who is sitting in the next table. You think you have an advantage to chat him/her up: You have got oreos. You think of offering him/her oreos in order to start a conversation. You are aware of the fact that more oreos you offer more chance you will have.

If you align the oreos using regular geometrical shape, which is the shape of egg case, you will see that only 6 oreos can fit on your napkin.

On the other hand if you use the geometrical shape of the fruit-vegetable case 8 oreos fit on the surface of the napkin.

Honeycomb

In the previous article I’ve told you about how honey bees found the most efficient geometrical shape for their honey storage. Just like honey bees, bazaar workers also found (consciously or not) the same shape for fruit-vegetable cases and stands. If that’s so, then how come do they use regular alignment for the egg cases?

That is because the most efficient alignment can vary when the shape of the case (or surface) is limited to some specific length:

This time I used a different-sized napkin for the oreos. Regular alignment let me align 9 oreos as honeycomb shape stuck to 8 oreos.

Then, as long as the area of the egg case stays the same, regular alignment will be the most efficient alignment. Kudos to the egg case producers.

One wonders…

Q: Let’s say you have 20 eggs. Each egg can sit into a space that has diameter of 4 cm. Which geometrical alignment would require less area for these 20 eggs?

M. Serkan Kalaycıoğlu

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