# Where Do You Put That Hat?

Yesterday, my father came to me with a math question. He had been hired by a Coast Guard Chief Petty Officer who wanted a wooden box for her hat. She wanted it to be an octagon with a height (h) of 8 inches and a diagonal (d) of 12 inches. My father had been trying to make this work for some time, but was stymied.

I don’t do a lot of geometry, but I smelled a rat. An octagon is a very symmetrical form with equal angles and sides. The 8/12 combo just didn’t seem like it would work.

So I went online and did a search for “octagon measurements.” It took me to this excellent site called Had 2 Know, which has an “octagon calculator. You enter any parameter and it tells you all the others. I entered 12 inches for the diagonal and it spit back a height of 11.1 inches. So there was a reason my dad couldn’t make those measurements work: they are inconsistent.

I thought a hexagon might work better. Thankfully, Had 2 Know also has a hexagon calculator. And I was right: a 12 inch diagonal would dictate a 10.4 inches height—better but still a long way off from 8 inches. It seems to me that a pentagon might be the way to go, but because it has an odd number of sides, it doesn’t make sense in this discussion.

It occurs to me that what is really desired is not an octagon, but an eight-sided box. After all, the human head is not round. Go look at a bowler, for instance: it is longer front to back than side to side to side. So one could create an oblong quasi-octagon. But frankly, this is madness. Who wants an eight sided hat box? It will be a storage nightmare. I think what our Guardian really wants is a rectangle.

Eight by twelve. Perfect!

Afterword

Where did you get that hat?!

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