Postal workers pose a special problem for end-of-year gift-giving: all sorts of rules govern the things they’re allowed to accept. Carriers are allowed to receive gifts worth up to $20 at a time, but not cash or cash equivalents, like gift cards, and never more than $50 in a calendar year.

Last year, we had the perfect gift for Mr. Handy, our long-time carrier down in Baltimore: a personalized copy of my children’s book, The Mighty Lalouche, which is about a tiny Parisian postman who just happens to be invincible in the boxing ring. As Mr. Handy put it, “Finally, I was able to read a book to my grandson where I was the hero!”

But this year, we were out of ideas. This can happen when you’ve been lucky enough to have the same wonderful postman for fifteen years. As I was brainstorming, my eye wandered to my bookshelf and came to rest on Extreme Origami by Won Park, a how-to guide to folding animals from dollar bills.

Then it hit me: the rule about gifts covered cash and cash equivalents, but it didn’t mention anything about artwork!

The projects in Extreme Origami were beyond my rudimentary skills, so I turned to Youtube and found a video that showed me how to transform a twenty dollar bill into a tiny, crisply folded short-sleeved shirt and tie. (If you go to Youtube and search for “improved origami dollar shirt,” you’ll find it, too.)

Sticklers for the rules will say, “But that’s still a cash gift! Not allowed.”

Art lovers, on the other hand, will say, “It ceased to be cash when you turned it into origami.”

I’m happy to let the ethicists duke it out. What Mr. Handy does — or doesn’t do — to my artwork in the privacy of his own home is up to him. And if the raw materials of my year-end origami gift prove useful to him in some way, so much the better…

Folding that little shirt and tie awoke my interest in origami, which has its roots in my childhood. I was fascinated by the transformation of flat paper into three dimensional sculptures. I remember spending hours in the basement with my origami book propped open, trying to make sense of the dots, dashes, and little round arrows that comprised the wordless instructions.

I didn’t know it at the time, but those folding symbols, which have become the standard notation for the craft, were a relatively recent development, the invention of a man named Akira Yoshizawa in post-war Japan. Origami is a tradition hundreds of years old, but until Mr. Yoshizawa’s standardized notation, there was no way to widely disseminate origami designs.

Once Yoshizawa’s system of universal symbols was adopted, origami became a truly international phenomenon. These days, it’s rare to meet a young person on any continent who hasn’t folded — or at least attempted to fold — a paper crane.

But the last twenty years have seen an explosion in the complexity of folded artwork, largely thanks to the discoveries of one man, Dr. Robert Lang, a physicist and engineer who turned his origami hobby into a new field of applied mathematics.

Dr. Lang’s twenty minute TED talk, “The Math and Magic of Origami,” which can be easily found with a Google search, is a profound treatise on the way aesthetics and science can overlap. It turns out that paper-folding is governed by four basic mathematical rules. Once you account for those rules, a universe of possibilities opens up. In the course of his talk, Dr. Lang shows slides of some of his more famous origami creations, including insects of astounding complexity.

But he also addresses the ways the principles of paper-folding can be applied to all sorts of engineering problems: for instance, how to fold a giant solar panel to fit inside the cone of a rocket. Or how to make a stent that’s small enough to slide easily through the human circulatory system but can pop open when it reaches its destination.

In the course of his research, Dr. Lang wrote a piece of software called TreeMaker that can transform virtually any stick figure you can draw into a foldable origami design. You can download a free copy of TreeMaker from his website, www.langorigami.com.

The website is worth a visit, even if you never attempt his trademark designs like the tarantula, the cloven-hoofed mountain goat, or the husband and wife praying mantises locked in a death struggle — all folded from a single sheet of paper with no cuts.

I’d like to close with a toast for 2015, inspired by Dr. Lang’s incredible creations: as a new year opens before us, here’s to following our curiosity — wherever it may lead!