Snow Crash

Last weekend we went on a family ski trip up to Vermont with Nick and some friends of his. It was mostly great. The skiing itself was awesome. The snow and the mountain were perfect and we all had a great time with the skiing. Michelle is really coming along, and Lizzy is doing good too. We stayed in a condo right on the mountain with Nick and his family, and that was a good time. Watched The Empire Strikes Back, Jeannie’s favorite movie of all time. On the other hand it was really cold the whole time, especially sitting on the lift as it approached the summit.

The big downer is we got into a bit of a road accident on the trip up. We got caught in a pileup on an off ramp. Luckily no one was hurt, but once we were done feeling relieved over that, the hassle factor set in. We had to wait an hour and half for the police to show up and get everyone’s statements. So we got up there pretty late on Friday. And we’ve been dealing with insurance and paperwork ever since. At first I thought the Jeep had only minimal damage; I just lost my license plate and maybe the fan was a bit noisy. The car in the middle, a Mini, seemed to fare the worst, with both bumpers (the flimsy plastic kind) cracked. The car in front, the cause of al of it, was another SUV and looked to be totally intact.

Close inspection later revealed a piece of framing behind my bumper was bowed. It did its job and bore the brunt of the impact. There’s other assorted minor damage, probably mostly not worth fixing on account of the car being so old. It’s safe and drives okay. I’ll take it to my local mechanic and get his opinion on the minimum necessary repairs, put the license plate back on myself and be done with it.

I guess I’ll start looking to replace the car this spring. I had hoped to keep it another year or so, since we just got a new car for Jeannie. It’s certainly good enough to get to the train station and back for a while, but longer term it’s transitioning to the beater category. Luckily time is on my side and I can research cars and wait for sales. Too bad cash for clunkers in no longer in effect!

Did I mention that the skiing part of the trip was really great? An since we’ve been back in town, it’s gotten really warm, like spring and almost half the snow from January has melted. On the way home from Vermont we saw another car crash at the exact same spot. I’m sure the police keep statistics as to how many accidents occur at the ramp. It’s be interesting to know.

A Little Thaw

It’s been up above freezing the last few days, a big relief and a tease that spring is not far off. Still plenty of big piles of snow on the ground though, even in midtown Manhattan. Even if it keeps on melting at this rate it’ll be another month before I see my lawn again.

Folding Pentagons

I’ve been working on an origami e-book that is on track to come out this spring. (More on that in a future post.) One of the models in it is my Fivefold Rose, which I’ve updated and improved. It’s based on a pentagon and the question of how to fold a regular pentagon from a square has been an age-old problem in origami. I know a few methods for approximating a regular pentagon, and with practice I’ve gotten good at eyeballing it so it comes out every time.

I recently discovered a new method in an old book from Japan from the 60’s. It’s been on my shelf for years, and I was on the verge of throwing it away and thought I’d flip thru it to see if there was anything worth saving it for, when I came across this little gem in the back of the book in with the classic bases. It’s based on the trick that the cosine of and 18 degree angle is within one percent of a 1:3 slope.

I’ve digrammed my own version of it, revising the steps to be clearer and more accurate, and making the folding sequence of subsequent steps reduce rather than amplify any folding errors. It’s pretty easy to get a perfect pentagon every time. The diagrams are essentially the first few steps of the new Fivefold Rose, thru forming the pentagon and some precreasing for the base.

The center of the pentagon is the center of the paper, which is useful for some applications. The tradeoff is that top corner of the pentagon is truncated (although you could just as easily fold a slightly smaller pentagon). For this model it doesn’t matter, and for alot of my pentagon-based polyhedra it doesn’t matter either. In any event it could easily be adapted to making a pentagon with the apex at the center of the top edge of the square by first folding the two long diagonals that would form the top point of a star embedded in the pentagon. I’m also exploring another method that uses the trick of the cosine of a 36 degree angle is very close to 4:5.

I showed it to John Montroll, the only other person I know who cares about this kind of thing like I do. In is book Origami Polyhedra Design he has a method for folding a golden rectangle from a square. The first time I saw it I immediately though there must be a way to use that to make a pentagon. It’s been in the back of mind ever since, but now I can forget about it. John has solved the problem and come up with a really elegant, mathematically perfect method for folding a pentagon in just 11 steps. Blew my mind when I saw it. Unfortunately you’ll have to wait for his next book to see it.

Have an Ice Day

You’d think that by now I’d have something else to talk about besides the bad weather. And I do, I swear. Origami and music stuff, but it’s all work in progress.

The bad weather is neverending. But even so it hasn’t run out of nasty new surprises yet. Today it was freezing and everything iced up bad. In my driveway an 18” high icicle formed sticking straight up like a stalagmite, from water dripping from the power line above. I went out to shovel, which meant mainly breaking up the ice, but left the icicle. Jeannie ran it over with her car.

For some reason Michelle was really excited about Ground Hog’s day. She woke up before daylight and brought her stuffed animals out to the couch to camp out and wait for it, like it was Xmas morning or a space shuttle launch or something. As I was getting up she’d already woken up Jeannie and the two of them were finding the feed from Punxsutawney, PA. So I witnessed the rodent prognosticate an early spring. Oy. Wait until she finds out the rodent doesn’t know jack.