math

82 Articles

Teaching Math With 3D Printers

October 25, 2025 by 10 Comments

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

July 20, 2025 by 24 Comments

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?

July 9, 2025 by 11 Comments

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

July 9, 2025 by 14 Comments

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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Illustrated scheme of Sam Ben Yaakovs concept

Leakage Control For Coupled Coils

June 5, 2025 by 3 Comments

Think of a circuit model that lets you move magnetic leakage around like sliders on a synth, without changing the external behavior of your coupled inductors. [Sam Ben-Yaakov] walks you through just that in his video ‘Versatile Coupled Inductor Circuit Model and Examples of Its Use’.

The core idea is as follows. Coupled inductors can be modeled in dozens of ways, but this one adds a twist: a tunable parameter 𝑥 between k and 1 (where k is the coupling coefficient). This fourth degree of freedom doesn’t change L₁, L₂ or mutual inductance M (they remain invariant) but it lets you shuffle leakage where you want it, giving practical flexibility in designing or simulating transformers, converters, or filters with asymmetric behavior.

If you need leakage on one side only, set 𝑥=k. Prefer symmetrical split? Set 𝑥=1. It’s like parametric EQ, but magnetic. And: the maths holds up. As [Sam Ben-Yaakov] derives and confirms that for any 𝑥 in the range, external characteristics remain identical.

It’s especially useful when testing edge cases, or explaining inductive quirks that don’t behave quite like ideal transformers should. A good model to stash in your toolbox.

As we’ve seen previously, [Sam Ben-Yaakov] is at home when it comes to concepts that need tinkering, trial and error, and a dash of visuals to convey. Continue reading “Leakage Control For Coupled Coils” →

Understanding Linear Regression

May 8, 2025 by 7 Comments

Although [Vitor Fróis] is explaining linear regression because it relates to machine learning, the post and, indeed, the topic have wide applications in many things that we do with electronics and computers. It is one way to use independent variables to predict dependent variables, and, in its simplest form, it is based on nothing more than a straight line.

You might remember from school that a straight line can be described by: y=mx+b. Here, m is the slope of the line and b is the y-intercept. Another way to think about it is that m is how fast the line goes up (or down, if m is negative), and b is where the line “starts” at x=0.

[Vitor] starts out with a great example: home prices (the dependent variable) and area (the independent variable). As you would guess, bigger houses tend to sell for more than smaller houses. But it isn’t an exact formula, because there are a lot of reasons a house might sell for more or less. If you plot it, you don’t get a nice line; you get a cloud of points that sort of group around some imaginary line.

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Deriving The Reactance Formulas

April 28, 2025 by 9 Comments

If you’ve dealt with reactance, you surely know the two equations for computing inductive and capacitive reactance. But unless you’ve really dug into it, you may only know the formula the way a school kid knows how to find the area of a circle. You have to have a bit of higher math to figure out why the equation is what it is. [Old Hack EE] wanted to figure out why the formulas are what they are, so he dug in and shared what he learned in a video you can see below.

The key to understanding this is simple. The reactance describes the voltage over the current through the element, just like resistance. The difference is that a resistance is just a single number. A reactance is a curve that gives you a different value at different frequencies. That’s because current and voltage are out of phase through a reactance, so it isn’t as easy as just dividing.

If you know calculus, the video will make a lot of sense. If you don’t know calculus, you might have a few moments of panic, but you can make it. If you think of frequency in Hertz as cycles per second, all the 2π you find in these equations convert Hz to “radian frequency” since one cycle per second is really 360 degrees of the sine wave in one second. There are 2π radians in a circle, so it makes sense.

We love developing intuition about things that seem fundamental but have a lot of depth to them that we usually ignore. If you need a refresher or a jump start on calculus, it isn’t as hard as you probably think. Engineers usually use vectors or imaginary numbers to deal with reactance, and we’ve talked about that too, if you want to learn more.