Category Archives: math

Understanding Math Rather Than Merely Learning It

There’s a line from the original Star Trek where Khan says, “Improve a mechanical device and you may double productivity, but improve man and you gain a thousandfold.” Joan Horvath and Rich Cameron have the same idea about improving education, particularly autodidacticism or self-learning. They share what they’ve learned about acquiring an intuitive understanding of difficult math at the Hackaday Superconference and you can watch the newly published video below.

The start of this was the pair’s collaboration on a book about 3D printing science projects. Joan has a traditional education from MIT and Rich is a self-taught guy. This …read more

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Posted in 2018 Hackaday Superconference, 3d Printer hacks, calculus, cons, Hackaday Columns, leibniz, math, newton, Supercon | Leave a comment

An Abstract Kind of Clock: The Chinese Remainder Clock

Hackaday likes clocks, a lot. Speaking personally, from my desk I can count at least eight clocks, of which seven are working. There’s normal quartz movement analog clocks, fun automatic wristwatches, run-of-the-mill digital clocks, a calculator watch, and a very special and very broken Darth Vader digital clock/radio combo that will get fixed one day — most likely. Every clock is great, and one of life’s great struggles is to see how many you can amass before you die. The more unique the clock is, the better, and nothing (so far) tops [Antonella Perucca]’s Chinese Remainder Clock.

What separates [Antonella …read more

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Posted in clock, clock hacks, math | Leave a comment

FxSolver is a Math Notebook for Engineers

If you like to rely on the web to do your electronics and computer math, you’ll want to bookmark FxSolver. It has a wide collection of formulae from disciplines ranging from electronics, computer science, physics, chemistry, and mechanics. There are also the classic math formulations, too.

When you first hit the page you’ll see a message that your solver is currently empty. There’s a sidebar on the left and a search box. To start, try searching for a few things you know you’ll want to use. We did Ohm’s law and a voltage divider, winding up with a custom page …read more

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Posted in calculator, formula, internet hacks, math, online | Leave a comment

Understanding Math vs Understanding Math

One of the things hard about engineering — electrical engineering, in particular — is that you can’t really visualize what’s important. Sure, you can see a resistor and an LED in your hands, but the real stuff that we care about — electron flow, space charge, and all that — is totally abstract. If you just tinker, you might avoid a lot of the inherent math (or maths for our UK friends), but if you decide to get serious, you’ll quickly find yourself in a numerical quicksand. The problem is, there’s mechanically understanding math, and intuitively understanding math. We recently …read more

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Posted in convolution, fourier series, fourier transform, math, misc hacks | Leave a comment

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.

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 …read more

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Posted in Interest, Jan Łukasiewicz, math, RPN, RPN calculator, sinclair scientific | Leave a comment

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. …read more

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Posted in homework, math, software hacks, wolfram alpha | Leave a comment

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 …read more

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Posted in linear algebra, math, multiplexing, resistors, systems of equations | Leave a comment

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.

As you might expect, 3D output takes a good bit of math, and the chip …read more

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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 …read more

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Posted in Interviews, math, polyhedra, sea shells | Leave a comment

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 …read more

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Posted in math, projection mapping, research, tokyo, university, video hacks | Leave a comment