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Sideband #70: The exp Function
Converging… Back in October I published two posts involving the ubiquitous exponential function. [see: Circular Math and Fourier Geometry] The posts were primarily about Fourier transforms, but the...
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Sideband #71: Matrix Math
There are many tutorials and teachers, online and off, that can teach you how to work with matrices. This post is a quick reference for the basics. Matrix operations are important in quantum mechanics,...
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Sideband #72: Trig Is Easy!
Trigonometry is infamously something most normal people fear and loath. Or at least don’t understand and don’t particularly want to deal with. (In fairness, it doesn’t pop up much in regular life.) As...
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Sideband #73: Complex 4D
I’ve written a number of posts about four-dimensional Euclidean space, usually in the context of one of my favorite geometrical objects, the tesseract. I’ve also mentioned 4D Euclidean spaces as just...
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Sideband #74: Volume and Surface Area
I’ve always had a strong curiosity about how things work. My dad used to despair how I’d take things apart but rarely put them back together. My interest was inside — in understanding the mechanism....
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Sideband #75: Electronic Shortcuts
My notes don’t include what triggered the thought, but I think it was something in one of the Lee Smolin books I read recently. My recent post, Analog Computing, brought the idea to mind again, because...
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Sideband #76: Fun with Op Amps
Last November I posted about electronics “shortcuts” — rules of thumb that help interpret, even design, a circuit. These are approximations of more complex behavior but work well enough for a first cut...
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Sideband #77: Speaking of Op Amps…
The last Sideband post (over eight months ago) was about Op Amps, mostly because I think they’re very cool but also easy to understand in the context of the Three Rules of Op Amps. [See this post and...
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Sideband #78: Watch Compass
Long ago (in the first year of this blog), I posted Sideband #34: The North Star, which was about how sighting on the North Star (Polaris) gives you your latitude. Simply put, the elevation of the star...
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Sideband #79: Growth Curves
nx vs xn vs nx (for n=42) You’ve probably heard the phrase “exponential growth” in reference to something that grows very fast. A common example is bacteria in a petri dish. More relevant in daily...
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Sideband #80: Divide by Zero
You may remember learning way back in grade school that you can’t divide by zero. You may remember being told that division by zero is undefined. But have you ever wondered why we can’t divide by zero?...
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Sideband #81: Tangent Cones
It’s been a while since my last Sidebands post. That’s partly because I’ve been working on a project that I’m sure will become a multi-post series and thought it would be nice to start with #81. But...
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