I got a nifty gift yesterday from one of my tutoring clients. It’s a pencil case. But not just any pencil case. It’s made of one giant continuous zipper. Check out my Zipit Monster Pouch:

As I was enjoying it, I began wondering a couple of things:

- What would it look like opened up?
- How long would it be opened up?

### There are two ways to solve the problem.

The temptation is to just unzip the thing and look. And indeed, that would be one way to answer my questions.

But if something like this hits your math class, consider approaching it “the hard way.”

What we know:

- Totally flat, the monster is 8.75 inches long and 4 inches wide.
- The diagonal from corner to corner is 9 inches.
- On each side, you can count 7 diagonals of zipper.

What we might need to know:

- What’s the angle of the diagonals?
- How does the zipper wrap around?

What might be fun to figure out:

- If I wanted a coin purse like this, how much zipper would I need?
- If I wanted a shoulder bag like this, how much zipper would I need?

### Can you use it as a lesson?

If you propose the questions to the class, can you use it as a Project Based Learning activity? There’s some serious geometry going on here!

Share your thoughts in the comments!

You can share that idea with your students because it is geometrically pretty, and you can choose to like any historical explanation, but keep in mind that the Summarians used sexgesimal notation well before the Babylonians (from whom they obtained it).

More importantly, the Chaldeans routinely made and preserved examples of solar and lunar eclipses dating as early as 652 BC. They also calculated the recurrence of these events in periods, synodic months, with a span of about 29 1/4 days. By the first century BC they had conceived the zodiac recognizing major star patterns that moved in approximately monthly cycles across the heavens. Hence a period of 12 synoptic months.

The base sixty system was coincident with the emergence of the 360 day year, but your suggestion would have more likely led to a zodiac like method of 6 periods, not twelve.

Wow, Pat. Thanks for the information!

The Babylonians knew the length of the year to be 365.25 days so anyone who claims that days-in-a-year had anything to do with it is a moron. They were quite competent at mathematics.

Far more likely is the idea that 360 is a really nice number, a highly composite number.

For people who worked with fractions instead of decimals, and who needed to subdivide a circle into many different sizes of piece (24) with integer sizes, 360 is the best choice.

I’m not sure if they should be called morons…

But since you are the Curmudgeon, we’ll run with it. ðŸ˜‰

Thanks for stopping by!