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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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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 #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 #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 #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 #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 #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 #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 #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 #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 #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 #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 #69: Inside a Tesseract
Four years ago I started pondering the tesseract and four-dimensional space. I first learned about them back in grade school in a science fiction short story I’d read. (A large fraction of my very...
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Sideband #68: More Fraction Digits
The last Sideband discussed two algorithms for producing digit strings in any number base (or radix) for integer and fractional numeric values. There are some minor points I didn’t have room to explore...
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Sideband #67: Fraction Digits in Any Base
Fractional base basis. I suspect very few people care about expressing fractional digits in any base other than good old base ten. Truthfully, it’s likely not that many people care about expressing...
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Sideband #66: Abacus Multiplication
Today’s earlier post got into only the beginnings of abacus operation — mainly how to add numbers. To demonstrate how they have more utility than just adding and subtracting, this Sideband tackles a...
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Sideband #65: 4D Rotation
This is a Sideband to the previous post, The 4th Dimension. It’s for those who want to know more about the rotation discussed in that post, specifically with regard to axes involved with rotation...
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Sideband #64: Matrix Magic
In the last installment I introduced the idea of a transformation matrix — a square matrix that we view as a set of (vertically written) vectors describing a new basis for a transformed space. Points...
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Sideband #63: Matrix Rotation
For me, the star attraction of March Mathness is matrix rotation. It’s a new toy (um, tool) for me that’s exciting on two levels: Firstly, it answers key questions I’ve had about rotation, especially...
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Sideband #62: Quaternions
Folded into the mixed baklava of my 2018, was a special mathematical bit of honey. With the help of some excellent YouTube videos, the light bulb finally went on for me, and I could see quaternions....
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