We always enjoy videos from the [Mathologer], but we especially liked the recent video on the Helicone, a toy with a surprising connection to mathematics. The toy is cool all by itself, but the video shows how a sufficiently large heliocone models many “natural numbers” and acts, as [Mathologer] puts it, acts as “microscope to probe the nature of numbers.”

The chief number of interest is the so-called golden ratio. A virtual model of the toy allows easy experimentation and even some things that aren’t easily possible in the real world. The virtual helicone also allows you to make a crazy number of layers, which can show certain mathematical ideas that would be hard to do in a 3D print or a wooden toy.

Apparently, the helicone was [John Edmark’s] sculpture inspired by DNA spirals, so it is no surprise it closely models nature. You can 3D print a real one.

Of course, the constant π makes an appearance. Like fractals, you can dive into the math or just enjoy the pretty patterns. We won’t judge either way.

We’ve seen math sequences in clocks that remind us of [Piet Mondrian]. In fact, we’ve seen more than one of those.