Here's another one where nature meets engineering on a microscopic scale: tiny submarines small enough to swim through your blood vessels.
Oops, wrong link.
The submarines I'm actually talking about won't carry people, but once built they could be made to carry small doses of medicine, and directed to swim to a specific spot in your body.
The reason this merits a mention in the "nature meets engineering" category is that down at the 10\(\mu\)m scale (which is to say, 100 of these lined up end to end would only reach 1mm long) you can't just build a tiny motor and propeller and expect to have the submarine go anywhere, because at that scale, the physics of it just doesn't work. Instead, what they looked at was how creatures that are actually that small get around.
A few years ago, I ran across an article which was based on a transcript of a lecture given in the mid-seventies, titled Life at Low Reynolds Numbers. (The Reynolds number being the ratio of inertial force to viscous force. We live at high Reynolds numbers, where inertia dominates and viscosity is irrelevant.
There's a recent video which covers some of the same material as well, with microscope video illustrating the single-celled creatures at the size we're talking about:
For us, dragging along a millimetre or so of water along our skin as we move really doesn't affect our swimming. For something that's 1/100th of a millimetre long, dragging even 1/10th of a millimetre of water along is incredibly heavy relative to its body weight, and water tends to stick to surfaces and to itself: that's viscosity. On top of that, the cell's body weight is so tiny that momentum is insignificant. "Objects in motion tend to remain in motion"? Not for these little creatures. You can see in the video above how abruptly things stop moving when the cells stop actively trying to move them.
So for this microscopic submarine, swimming around like a bacterial cell is a necessity. It's swimming around in the macroscopic equivalent of honey or molasses—difficult at best, because at the low Reynolds numbers here, viscosity dominates and inertia is irrelevant. The water doesn't actually change to get as thick as molasses, of course; it's just that on the micron scale, water sticks to itself very well, but the micron scale is irrelevant to our experience. I'm sure a bacterial cell, were it to suddenly find itself expanded to our scale, would find the notion of not halting as soon as it stopped trying to move equivalently counterintuitive.