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.
Mathematics were always meant to be interpreted visually
Source? Some people think visually, some don’t. Also, the invention of language for scientific concepts is not a trivial process, and visual representations may be stopgaps while language is catching up.
The source would be every system of conveying math, especially for trade. The majority of surviving early structured writing are trade documents and contracts.
For me seeing a short film in middle school math class showed me in such little time something that all the book bound numbing numbers and teacher talk simply failed at. Absolutely!
Math-dyslexia was rediscovered early in this century but they knew about it in the 1930’s. Should such students be exempted from heavy math courses and be steered towards worthwhile studies?
It’s no different than being physically handicapped and phys-ed classes.
I was diagnosed back then and of course they came to no conclusion. You’ll just have to try harder at math bla bla blah. Then why could I know the answer in a lot of visual geometry problems and everyone else had to “do the math” the hard way and even then had no idea what it’s about.
The term for it is Dyscalculia, and it has some interesting software based treatment attempts. As usual, wikipedia has a good overview https://en.wikipedia.org/wiki/Dyscalculia
Fantastic! Love this post and will pursue similar models, both virtual and physical. Thanks.
Absolutely the best video I’ve watched in a long time.. thank you for your efforts making mathematical and visual magic mesh with Christmas cheer!