I have just found an awesome way of embedding cross-browser math in a webpage: MathJax using AsciiMathML syntax. All you have to do is add a call to the MathJax JS library using their CDN call, and enclose a math expression in backticks(`), using the ASCIIMath syntax, which is easily summarized on one page; MathJax does the rest, to make the math show up cross-browser.

## home electrolysis

I like hydrogen. And I thought it might be interesting to separate some out from water, with the hope that I could fill two balloons (one with oxygen, one with hydrogen), and later ignite them to see which gave the more interesting burn (the potential boom). After some failed setups, I decided against separate collection; besides, putting the H_{2} and O_{2} in the same container would provide a ready source of oxygen for the combustion.

## sieve of eratosthenes

“Do you want to play a game on the chalkboard?” I asked this question after we’d read The Boy Who Loved Math for the umpteenth time, and I thought they might enjoy seeing how the sieve, which was featured in an illustration in the book, was made. I doubt much stuck, but they seemed to enjoy taking turns crossing out numbers. ðŸ™‚

## duploÂ® photosynthesis

The kids were reading a book which mentioned photosynthesis, and they asked how it works. I gave them the quick “the plant turns sunlight, water, CO_{2} into sugar, which it uses for engery.” That wasn’t enough for them. SO I went to the chalkboard and did a quick stoichiometry; then I got out some handy DuploÂ® bricks, made some water and CO_{2} molecules, which I put on a DuploÂ® base, to act as the leaf. Our hands became the sunlight, and we â€¦ disassociated â€¦ those molecules. ðŸ™‚ Then I rebuilt them into sugar* molecules that went deeper into the plant, and O_{2 }molecules back into the air. They seemed to like that explanation.

## antigravity spoon

So, as my daughter dropped her spoon at a meal yesterday, my son suggested we get her an anti-gravity spoon. I am a blessed man. ðŸ™‚

I started thinking about the fact that people rarely think through the implications of suddenly defeating gravity’s pull on a single object. Namely, that it’s *gravity* that’s providing the centripetal force to keep it moving with the planet.

## antigravity spoon derivations

This is the derivation for my main “antigravity spoon” entry.

Continue reading antigravity spoon derivations

## hilbert 3d

Robert Dickau’s “Hilbert 3D curve, iteration 3” (CC BY-SA)

I’ve been a fan of fractals since high school (and have even read Mandelbrot’s Fractal Geometry of Nature). One of my favorite fractals is the Hilbert Curve. Many articles I’ve found try to explain how to generate a 3D version of the curve… but none to my satisfaction (meaning, they lost me at some point): mostly, because they seemed to be focused on an iterative loop to describe it, when it’s simplest to describe in terms of a recursive algorithm. Studying Dickau’s 3D image from the Hilbert Curve Wikipedia page, I was able to come up with a recursive 3D pseudo-turtle algorithm to draw it, and came up with a few other thoughts.

## divisible by 3: sum of digits

I was taught that numbers that are divisible by 3 (or 9) will have the sum of their digits divisible by 3 (or 9) all the way down to one digit. But *why* do these numbers behave that way?

Continue reading divisible by 3: sum of digits

## bottomless pit: ultimate bungee

So a radio host’s silly quiz game had the failing caller “fall into a bottomless chasm” or some such phrasing. That got me thinking: it’s bottomless, so there is nothing downwards from it; but if it’s truly bottomless, you’d go through the center of the earth, at which point you could hit a “ceiling” at a rather high speed, since you’d be going upwards at this point. But if there were no ceiling, that would be like ultimate bungee! Continue reading bottomless pit: ultimate bungee

## hydrogen combustion

I drive a Mazda RX-8, and ever since I heard about the RX-8 Hydrogen RE, I’ve wished it had made it into production in the United States. Every once in a while, I’ve googled to see if there’s anybody who converts RX-8’s to dual-fuel hydrogen, but I’ve not found any yet.