So, my wife and daughter were taking some squares of fabric to make a 3×3 quilt for a doll that’s going in an Operation Christmas Child shoebox. My wife asked me if it were possible, using 3 of each square, to not have any repeats in any row or column, and not to have a diagonal that’s solid. In short, the answer is no. Continue reading 3×3 Quilt: n-Tile n×n checkerboards

# Tag: math

## Reuleaux Triangles (Generalized) — Triangles with ZoomZoom

I’m a fan of a nice rounded triangle: the Wankel-based rotary engines found in the Mazda RX-7 and RX-8 use a rounded triangle, and I’ve owned one of each. And there’s the mathematically more pure Reuleaux triangle, which is a curve of constant width, which gives it some nice mathematical properties.

Continue reading Reuleaux Triangles (Generalized) — Triangles with ZoomZoom

## π Day

π id one of my favorite numbers (e^{iπ}=0-1 show my favorite numbers, in no order of preference), so you’d think that I’d be a huge fan of π day — but I’m not.

## ripple

Some time ago, I tried coming up with my own water-drop/ripple simulation for making a small animated-gif background (akin to the moving backgrounds, like clouds, ocean breakers, etc, that are so popular as church lyric-projector backgrounds right now). Basically, I had a sinusoidish curve, decaying with radius and time; I simulated a dozen or so of these drips, usually centered off-picture, and added the curves; it made for some nice randomish moving water-surface. (Sorry, I cannot find where I put it for now.)

## PseuDoKu

“PseuDoKu” = What I’m calling variants of sudoku, whether simplificiation of or extrapolation from the original.

My daughter enjoys playing the “number game” on my phone with me; I tell her where to put the next solved number (“put a 2 between the 5 and the 6 in that grey box”, etc.). I’ve thus started doing simpler grids on the chalkboard — with just a 4×4 grid, and one number missing from each row or column, and haven’t made the logic require one-of-each-per-2×2. The other day, she asked for “1 to 5” instead of “1 to 4”: since I haven’t introduced her to the boxes, the fact that 5×5 cannot have the sub-box regions is irrelevant.

## PseuDoKu Details

What I’m calling variants of sudoku, whether simplificiation of or extrapolation from the original.

My daughter enjoys playing the “number game” on my phone with me; I tell her where to put the next solved number (“put a 2 between the 5 and the 6 in that grey box”, etc.). I’ve thus started doing simpler grids on the chalkboard — with just a 4×4 grid, and one number missing from each row or column, and haven’t made the logic require one-of-each-per-2×2. The other day, she asked for “1-5” instead of “1-4”: since I haven’t introduced her to the boxes, the fact that 5×5 cannot have the sub-boxes is irrelevant.

## mathjax

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.

## 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. 🙂

## 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. 🙂

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