The word “algorithm” can sometimes seem like a word designed to scare people away from math classes, much like the words “calculus”, “Fourier transform”, or “engineering exam”. But in reality it’s just a method for solving a specific problem, and we use them all the time whether or not we realize it. Taking a deep […]
Most people know about the numerical constant pi (or π, if you prefer). But did you know that pi has an evil twin represented by the symbol ϖ? As [John Carlos Baez] explains, it and its related functions are related to the lemniscate as pi relates to circles. What’s a lemniscate? That’s the proper name […]
Many languages feature a random number generator library for help with tasks like rolling a die or flipping a coin. Why, you may ask, is this necessary when humans are perfectly capable of randomly coming up with values? [ex-punctis] was curious about the same quandary and decided to code up an experiment to test the […]
Anybody interested in building their own robot, sending spacecraft to the moon, or launching inter-continental ballistic missiles should have at least some basic filter options in their toolkit, otherwise the robot will likely wobble about erratically and the missile will miss it’s target. What is a filter anyway? In practical terms, the filter should smooth […]
If you ask most people to explain the Fourier series they will tell you how you can decompose any particular wave into a sum of sine waves. We’ve used that explanation before ourselves, and it is not incorrect. In fact, it is how Fourier first worked out his famous series. However, it is only part […]
You’ve probably used Wolfram Alpha and maybe even used the company’s desktop software for high-powered math such as Mathematica. One of the interesting things about all of Wolfram’s mathematics software is that it shares a common core engine — the Wolfram Engine. As of this month, the company is allowing free use of the engine […]
If we are hiring someone such as a carpenter or an auto mechanic, we always look for two things: what kind of tools they have and what they do when things go wrong. For many types of embedded systems, one important tool that serious developers use is the Kalman filter. It is also something you […]
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 […]