Tag Archives: geometry

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. (The irony is that I began my corporate career arc as a hardware repair technician.)

My curiosity includes a love of discovery, especially unexpected ones, and extra especially ones I stumble on myself. It’s one thing to be taught a neat new thing, but a rare delight to figure it out for oneself. It’s like hitting a home run (or at least a base-clearing double).

Recently, I was delighted to discover something amazing about spheres.

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Wow to the Wow

Wow. April First, but it’s no joke how much — and how quickly — life changed. March 2020 changed the world. Now we’ll see if we survive it.

Spirits seem high around here. On my morning walk, in the park I saw that someone had used colored chalk to write good thoughts on the asphalt path: “Stay Positive!” “Nature!” “Yay! Vit. D.” “Family Time” “Exercise!” (Maybe others will join in. I think I have some colored chalk…)

It’s hard to top the real life wows, but I do have a few interesting items that might at least offer something of a distraction.

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Pondering Going Around

I’ve been hinting all month about rotation, and the time has finally come to dig into the topic. As mentioned, my interest began with wanting to understand what it means to rotate a tesseract — particularly what’s really going on in a common animation that I’ve seen. What’s the math there?

This interest in rotation is part of a larger interest: trying to wrap my head around the idea of a fourth physical dimension. (Time is sometimes called the fourth dimension, but not here.) To make it as easy as possible, for now I’m focusing only on tesseractae, because “squares” are an easy shape.

After chewing at this for a while (the tesseract post was late 2016), just recently new doors opened up, and I think this journey is almost over!

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Hunting Tesseracti

tesseract-00If you’re anything like me, you’ve probably spent a fair amount of time wondering what is the deal with tesseracts? Just exactly what the heck is a “four-dimension cube” anyway? No doubt you’ve stared curiously at one of those 2D images (like the one here) that fakes a 3D image of an attempt to render a 4D tesseract.

Recently I spent a bunch of wetware CPU cycles, and made lots of diagrams, trying to wrap my mind around the idea of a tesseract. I think I made some progress. It was an interesting diversion, and at least I think I understand that image now!

FWIW, here’s a post about what I came up with…

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Beautiful Math

Take a moment to gaze at Euler’s Identity:

Eulers Identity

It has been called “exquisite” and likened to a “Shakespearean sonnet.” It has earned the titles “the most famous” and “the most beautiful” formula in all of mathematics, and, in a mere seven symbols, symbolizes much of its foundation.

Today we’re going to graze on it!

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Happy Tau Day!

tau-1This might seem like another math post… but it’s not! It’s a geometry post! And geometry is fun, beautiful and easy. After all, it’s just circles and lines and angles. Well, mostly. Like anything, if you really want to get into it, then things can get complex (math pun; sorry). But considering it was invented thousands of years ago, can it really be that much harder than, say, the latest smart phone?

Even the dreaded trigonometry is fairly simple once you grasp the basic idea that the angles of a triangle are directly related to the length of its sides. (Okay, admittedly, that’s a bit of a simplification. The (other two) angles of a right-angle triangle are directly related to the ratios of the length of its sides, but still.)

However, this isn’t about trig; this is about tau!

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BB #19: Pixel Bubbles

Random pixels!

Random (inexpensive) pixels!

I’ve been listening to U2 all evening, so I’m energized, and you get a bonus post today.

The last two posts used a lot of words, so I need to let the word barrel fill up a bit before I use too many more.

(And as you know, work really taps into the barrel, so word conservation is really important. I recycle many of the words I use, and there’s that old trick of putting a brick in your mouth to cut down on word dumps.)

But pixels are really inexpensive these days, and they come in a wide variety of colors. I’ve arranged a bunch of them in some interesting patterns you might enjoy!

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