Reverse Polish Notation and its Mildly Confusing Elegance

The best rummage sale purchase I ever made was a piece of hardware that used Reverse Polish Notation. I know what you’re thinking… RPN sounds like a sales gimmick and I got taken for a fool. But I assure you it’s not only real, but a true gem in the evolution of computing.

Best rummage sale find ever!
Best rummage sale find ever!

Sometime in the 1980s when I was a spotty teen, I picked up a calculator at a rummage sale. Protected by a smart plastic case, it was a pretty good condition Sinclair Scientific that turned out when I got it home to have 1975 date codes on its chips, and since anything with a Sinclair badge was worth having it became mine for a trifling amount of money. It had a set of corroded batteries that had damaged one of its terminals, but with the application of a bit of copper strip I had a working calculator.

And what a calculator! It didn’t have many buttons at a time when you judged how cool a scientific calculator was by the prolific nature of its keyboard. This one looked more akin to a run-of-the-mill arithmetic calculator, but had button modes for trigonometric functions and oddly an enter key rather than an equals sign. The handy sticker inside the case explained the mystery, this machine used so-called Reverse Polish Notation, or RPN. It spent several years on my bench before being reverently placed in a storage box of Sinclair curios which I’ve spent half a day turning the house over to find as I write this article.

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Hand-Carving Geometric Art

[Scott Cramer] is a retired professional woodworker who specializes in geometric art made from beautifully joined wood. In this project he’s carving four interlocked cloverleaf rings from a block of basswood. First he made a series of cuts to turn the block into a cuboctahedron, a geometric solid comprising six squares and eight triangles. Then he drew on the basic lines of the rings on the wood and went to work with a chisel, smoothing and separating the rings and carving out the interior. You can see more shots of the project on his Facebook post, which is included after the break.

To see more of [Scott]’s projects you can follow his Twitter feed. Our favorites include this 70″ pentagonal icosatetrahedron built out of hemlock that [Scott] says is the “largest in Coös County, NH” — what, there are others? He also made a magogany representation of a Hamiltonian circuit of a dodecahedron’s vertices.

We love math art on Hackaday — see our interview with Francisco do Comité we ran earlier this year.

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Wolfram Alpha Shows its Work

The bane of math students everywhere is the teacher asking for you to show your work. If you’ve grown up where a computer is a normal part of school work, that might annoy you since a lot of tools just give you an answer. We aren’t suggesting you cheat at homework, but we did notice that Wolfram Alpha now shows more of its work when it solves many common math problems.

Granted, the site has always shown work on some problems. However, a recent update shows more intermediate steps and also covers more kinds of problems in a step-by-step format. There are examples, but be aware that for general use, you do need to upgrade to pro (about $6 a month or less if you are student or teacher).

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New Method for Measuring Lots of Resistors Using Very Few Wires

[Daqq] is back at it again with the linear algebra, and he’s now come up with a method for determining the resistance of lots of resistors using little of wires and loads of math.

Like any reasonable person, [daqq] decided it would be fun to “solve one of those nasty [electrical engineering] puzzles/exercises where you start out with a horrible mess of wires and resistors and you are supposed to calculate the resistance between two nodes.” You know, just an average Saturday night. At the time, he was also fascinated by Charlieplexing – an awesome technique that either allows one to control multiple polarized components, such as LEDs, simply by connecting them in a specific way. After toying with the idea for a while, [daqq] found that using just Charlieplexing would be“a horrible mess” but he didn’t stop there. Drawing inspiration from Charlieplexing, he came up with the idea to connect things in such a way that every node is connected by one connection to every other node – a complete graph from a topological view point (this makes so much more sense visually). From here, he was able to set pins to HIGH, LOW, or INPUT and gather all the data needed to solve his linear system of equations.

Now, there is a balance to everything, and while this system can determine the resistance of .5*N(N-1) resistors using just N wires, it also a memory and computation hungry method. Oh well, can’t have it all. But, while it’s computationally hungry, [daqq] got it working on an ATMega32, so it’s not an unmanageable feat. And, let’s not forget to mention [daqq’s] wonderful writing. Even if you don’t know linear algebra (or would rather forget), it’s a good read from a theory perspective. So good, in fact, that [daqq] is getting published in Circuit Cellar!

We love to see theory in the hacker world, so keep it coming! But, while we wait (wink wink), there’s always time to review the basic Hacker Calculus and check out our past math-related articles.

ATMega328 3D!

Small OLED displays are inexpensive these days–cheap enough that pairing them with an 8-bit micro is economically feasible. But what can you do with a tiny display and not-entirely-powerful processor? If you are [ttsiodras] you can do a real time 3D rendering. You can see the results in the video below. Not bad for an 8-bit, 8 MHz processor.

The code is a “points-only” renderer. The design drives the OLED over the SPI pins and also outputs frame per second information via the serial port.

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Interview: Francesco de Comité Makes Math Visually Awesome

Francesco de Comité is an Associate Professor in Computer Science at the University of Sciences in Lille, France, where he researches the 2D and 3D representation of mathematical concepts and objects. He’s presented papers on a variety of topics including anamorphoses, experiments in circle packing, and Dupin cyclides. His current project involves modeling and 3D printing sea shells. He’ll be presenting a paper on the topic at Bridges Conference in July. You can find his projects on Flickr as well as on Shapeways.

Hackaday: One of your recent projects involves creating fractal patterns and warping them into biologically-correct sea shell shapes, which you then print.

FdC: Modeling seashell shapes is an old topic–Moseley, 1838, D’Arcy Thompson beginning of 20th century. A seashell can be defined as a curve turning around an axis, while translating in the direction of this axis (i.e. on a helicoidal trajectory), and growing in size at the same time. This was modeled for computers in the ’60s by David Raup.

Drawing patterns on seashells was described by Hans Meinhardt using a model of chemical reactions (activator-inhibitor), in the same spirit as Turing’s work on morphogenesis. Combining these two works, and using 3D printers instead of 2D renderers, we can build realistic seashells, either by copying existing shells, or inventing new ones. A 3D model is not just a juxtaposition of a huge number of 2D views: manipulating 3D models can help you understand the object, find details, and so on.

I was curious to see if making a 3D seashell was possible. Moreover, I show that this can be done with simple tools — well, except the 3D printer.
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Projection Mapping in Motion Amazes

Projection mapping is pretty magical; done well, it’s absolutely miraculous when the facade of a building starts popping out abstract geometric objects, or crumbles in front of our very eyes. “Dynamic projection mapping onto deforming non-rigid surface” takes it to the next level. (Watch the video below.)

A group in the Ishikawa Watanabe lab at the University of Tokyo has a technique where they cover the target with a number of dots in an ink that is only visible in the infra-red. A high-speed (1000 FPS!) camera and some very fast image processing then work out not only how the surface is deforming, but which surface it is. This enables them to swap out pieces of paper and get the projections onto them in real time.

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