An Introduction To Analog Filtering

One of the major difficulties in studying electricity, especially when compared to many other physical phenomena, is that it cannot be observed directly by human senses. We can manipulate it to perform various tasks and see its effects indirectly, like the ionized channels formed during lightning strikes or the resistive heating of objects, but its underlying behavior is largely hidden from view. Even mathematical descriptions can quickly become complex and counter-intuitive, obscured behind layers of math and theory. Still, [lcamtuf] has made some strides in demystifying aspects of electricity in this introduction to analog filters.

The discussion on analog filters looks at a few straightforward examples first. Starting with an resistor-capacitor (RC) filter, [lcamtuf] explains it by breaking its behavior down into steps of how the circuit behaves over time. Starting with a DC source and no load, and then removing the resistor to show just the behavior of a capacitor, shows the basics of this circuit from various perspectives. From there it moves into how it behaves when exposed to a sine wave instead of a DC source, which is key to understanding its behavior in arbitrary analog environments such as those involved in audio applications.

There’s some math underlying all of these explanations, of course, but it’s not overwhelming like a third-year electrical engineering course might be. For anyone looking to get into signal processing or even just building a really nice set of speakers for their home theater, this is an excellent primer. We’ve seen some other demonstrations of filtering data as well, like this one which demonstrates basic filtering using a microcontroller.

How To Use That Slide Rule

You have that slide rule in the back of the closet. Maybe it was from your college days. Maybe it was your Dad’s. Honestly. Do you know how to use it? Really? All the scales? That’s what we thought. [Amen Zwa, Esq.] not only tells you how slide rules came about, but also how to use many of the common scales. You can also see his collection and notes on being a casual slide rule collector and even a few maintenance tips.

The idea behind these computing devices is devilishly simple. It is well known that you can reduce a multiplication operation to addition if you have a table of logarithms. You simply take the log of both operands and add them. Then you do a reverse lookup in the table to get the answer.

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The Sanskrit Square Root Algorithm

Years ago, no math education was complete without understanding how to compute a square root. Today, you are probably just reaching for a calculator, or if you are writing a program, you’ll probably just guess and iterate. [MindYourDecisions] was curious how people did square roots before they had such aids. Don’t remember? Never learned? Watch the video below and learn a new skill.

The process is straightforward, but if you are a product of a traditional math education, you might find his terminology a bit confusing. He will refer to something like 18b meaning “a three-digit number where the last digit is b,” not “18 times b,” as you might expect.

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Teaching Math With 3D Printers

We’ve often thought that 3D printers make excellent school projects. No matter what a student’s interests are: art, software, electronics, robotics, chemistry, or physics, there’s something for everyone. A recent blog post from [Prusa Research] shows how Johannes Kepler University is using 3D printing to teach math. You can see a video with Professor [Zsolt Lavicza] explaining their vision below.

Instead of relying on abstract 3D shapes projected on a 2D screen, GeoGebra, educational math software, creates shapes that you can produce on a 3D printer. Students can physically handle and observe these shapes in the real world instead of on a flat screen.

One example of how the 3D printer finds use in a math class is producing “Genius Square,” a multilevel tic-tac-toe game. You can find the model for that and other designs used in the classes, on Printables. Some prints are like puzzles where students assemble shapes from pieces.

Putting 3D printers in school isn’t a new idea, of course. However, machines have become much simpler to use in recent years, so maybe the time is now. If you can’t find money for printers in school, you can always teach robotics using some low-tech methods.

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8 Bit Mechanical Computer Built From Knex

Long before electricity was a common household utility, humanity had been building machines to do many tasks that we’d now just strap a motor or set of batteries onto and think nothing of it. Transportation, manufacturing, agriculture, and essentially everything had non-electric analogs, and perhaps surprisingly, there were mechanical computers as well. Electronics-based computers are far superior in essentially every way, but the aesthetics of a mechanical computer are still unmatched, like this 8-bit machine built from K’nex.

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No Tension For Tensors?

We always enjoy [FloatHeadPhysics] explaining any math or physics topic. We don’t know if he’s acting or not, but he seems genuinely excited about every topic he covers, and it is infectious. He also has entertaining imaginary conversations with people like Feynman and Einstein. His recent video on tensors begins by showing the vector form of Ohm’s law, making it even more interesting. Check out the video below.

If you ever thought you could use fewer numbers for many tensor calculations, [FloatHeadPhysics] had the same idea. Luckily, imaginary Feynman explains why this isn’t right, and the answer shows the basic nature of why people use tensors.

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Kids Vs Computers: Chisanbop Remembered

If you are a certain age, you probably remember the ads and publicity around Chisanbop — the supposed ancient art of Korean finger math. Was it Korean? Sort of. Was it faster than a calculator? Sort of. [Chris Staecker] offers a great look at Chisanbop, not just how to do it, but also how it became such a significant cultural phenomenon. Take a look at the video below. Long, but worth it.

Technically, the idea is fairly simple. Your right-hand thumb is worth 5, and each finger is worth 1. So to identify 8, you hold down your thumb and the first three digits. The left hand has the same arrangement, but everything is worth ten times the right hand, so the thumb is 50, and each digit is worth 10.

With a little work, it is easy to count and add using this method. Subtraction is just the reverse. As you might expect, multiplication is just repeated addition. But the real story here isn’t how to do Chisanbop. It is more the story of how a Korean immigrant’s system went viral decades before the advent of social media.

You can argue that this is a shortcut that hurts math understanding. Or, you could argue the reverse. However, the truth is that this was around the time the calculator became widely available. Math education would shift from focusing on getting the right answer to understanding the underlying concepts. In a world where adding ten 6-digit numbers is easy with a $5 device, being able to do it with your fingers isn’t necessarily a valuable skill.

If you enjoy unconventional math methods, you may appreciate peasant multiplication.

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