When droplets of melted snow drip down an icicle, they release small amounts of heat as they freeze. Heated air travels upwards and helps slow down the growth of the icicle’s top, while the tip is growing rapidly. Icicles can be dangerous and deadly, yet they can create some of the most amazing winter scenes. And for scientists, those winter scenes are playgrounds for discovery. We all know icicles form when melting snow begins dripping down a surface. But what scientists didn’t know is how their shape is formed. What makes each icicle different?

Icicles have a certain mathematical shape, and this mathematical shape is universal among icicles. So what is the math behind an icicle? The height is proportional to the radius to the four-thirds. What does the formula have to do with an icicle’s shape? It kind of looks like a carrot, it starts out flat and then goes up as you go.

As water drips onto an icicle and freezes, it releases heat. The warm air rises up the sides of the icicle. That warm air layer acts like a blanket that’s an insulator, and so the blanket is very thin near the tip and thick at the top. That allows the top to grow very slowly and the tip to grow rapidly — creating a long, thin icicle.