Category Archives: Mathematics

The dominant topic of my blog. You figured that out from the blog’s name, though, right?

Count the Dots!

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I’ll be nice, and not name names, but there was a time, when I taught at another school, when I had in-school suspension for half a day, every school day, for an entire semester. It sucked.

There was a senior in this high-school version of, well, jail, who was working on Geometry homework. I was trying to help him — and to get him to think for himself. (I’m always trying crazy stuff like that.)

To do the problem he was working on, he had to know what three times eight equals. He was 18, or perhaps 19, and a senior. I was not willing to simply tell him the product of three and eight, because . . . that’s just ridiculous.

I told him to draw a row of eight dots on his paper. He did. I told him to draw another such row beside the first row. He did. I told him, finally, to add a third row. He did, and gave me an utterly blank look.

I said, “Now count the dots.” He did.

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Even though he got the correct answer, he was still furious at me for, well, possibly the rest of his life, which may or may not still be going on. We haven’t kept in touch.

Rotating Zonish Polyhedron

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Rotating Zonish Polyhedron

Creating zonish polyhedra (related to zonohedra) and creating rotating polyhedral .gifs are two features newly added to Stella, the program used to make this, which may be tried for free at http://www.software3d.com/stella.php

How To Age Slowly

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This is the day I turn 45, and I still get carded when I buy beer. Those are my qualifications to write on this subject.

My first pieces of advice are to avoid tobacco altogether, and to moderate use of alcohol. I’ve seen people age prematurely, due to both factors, right in front of me (over a period of years), and it’s frightening. It’s also unnecessary, since these are both choices.

We also choose what we eat. My choices are limited by food allergies, though, forcing me lower on the food chain. I cannot eat mammals (nor shrimp) with becoming seriously ill, so I simply don’t eat beef, pork, etc. Perhaps this helps. It certainly cannot hurt.

Dysfunctional relationships make people unhappy, and unhappy people seem to age more quickly. I have found leaving bad relationships to be a most effective way of initiating (temporary, I hope) apparent reverse-aging, with the result that I look younger now than I did five or ten years ago.

I also feel younger. Are there aches and pains? Yes, there are, but they were worse at 35. I have chronic pain from a fall, and the resulting neck injury. Ten years ago, I was begging doctors for prescriptions for painkillers. Now, ibuprofen, stretching, and the occasional visit to my chiropractor give me the relief I need.

I think I would look 65 (or be dead) if I had not sought mental health treatment years ago, so getting such help, if you need it, is part of my advice. The problem here is often that people fear the stigma of mental illness, and delay seeking help, or avoid it altogether. Fighting back, to weaken that stigma, is the reason I write publicly on such subjects.

Another idea is a birthday ritual I have which, I must admit, can’t seriously be suggested as something that helps me age slowly, but it can’t hurt, either, and it’s fun. I make a star-design every year on my birthday, based on my new age. Here, therefore, is a star-design with 45 points:

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There is also an anti-aging attitude some people adopt, and I am one of them. This is a voluntary, deliberate refusal to stop being, in some senses (if not others), young. This can manifest itself in many ways; perhaps my star-ritual is one of them. Life is a game, of course, and I happen to like games — a lot.