The Helicone: Toy or Mathematical Oddity?

-

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.



from Blog – Hackaday https://ift.tt/iLwZAfP

Comments

Post a Comment

Popular posts from this blog

Modern Radio Receiver Architecture: From Regenerative to Direct Conversion

-
Image
Modern radio receivers have a distinct advantage over the common early designs which I covered in my previous article . Most of the receivers you will have worked with over the past couple decades are designs by Edwin Armstrong ; regenerative, superregenerative, or most commonly superheterodyne. These are distinguished by a few fascinating key traits that bring both benefits and drawbacks. Today let’s dive into Mr. Armstrong’s receivers. I’ll also talk about DC receivers which, despite the name, are not made to listen to batteries. These are receivers you are much more likely to encounter in modern equipment. Regenerative and Superregenerative The regenerative receiver is all about doing more with less. You still see some of these in simple applications like RF remote controls. The idea derives from how an oscillator works. In a simple way of thinking, an oscillator is an amplifier with enough positive feedback that any tiny signal at the right frequency will amplify and then, throu...
Get this one»

Hackaday Links: May 31, 2020

-
We begin with sad news indeed as we mark the passing of Marcel van Kervinck on Monday. The name might not ring a bell, but his project, the Gigatron TTL computer , certainly will. We did a deep dive on the microprocessor-less computer a while back, and Marcel was a regular at conferences and on the Gigatron forums, supporting users and extending what the computer can do. He was pretty candid about his health issues, and I’ll add that when I approached him a few weeks ago out of the blue about perhaps doing a Hack Chat about Gigatron, he was brutally honest about how little time he had left and that he wouldn’t make it that long. I was blown away by the grace and courage he displayed. His co-conspirator Walter Belger will carry on the Gigatron mission, including joining us for a Hack Chat on June 24. In the meantime, this might be a great time to pick up a Gigatron kit before they’re all sold out and get busy soldering all those delicious through-hole TTL chips. May of 2020 is the mo...
Get this one»

Homebrew 68K Micro-ATX Computer Runs Its Own OS

-
Image
We’re no stranger to home built Motorola 68000 computers here at Hackaday, but more often than not, they tend to be an experiment in retro minimalism. The venerable processor is usually joined by only a handful of components, and there’s an excellent chance they’ll have taken up residence on a piece of perfboard. Then [NotArtyom] sent in his Blitz , and launched the bar into the stratosphere. Make no mistake, the Blitz isn’t just some simple demo of classic chips. The open hardware motherboard has onboard floppy, IDE, and PS/2 interfaces, with a trio of 8-bit ISA expansion slots for good measure. The  Motorola 68030 CPU is humming along at 50 MHz, with 4 MB of RAM and 512 KB of ROM along for the ride. Designed to fit the Micro-ATX motherboard standard, you can even mount the Blitz in a contemporary PC case and run it on a standard ATX power supply. An earlier prototype of the Blitz motherboard. As if the hardware wasn’t impressive enough, [NotArtyom] went ahead and created hi...
Get this one»