Nidaros Cathedral Hypercube

This lamp (one of several) in front of the Nidaros Cathedral in Trondheim bears a striking resemblance to a hypercube.

Magic Static Cat

Two pieces of transparency film printed with static, taped on opposite sides of a piece of glass. From the right angle, the static aligns and the Cheshire Cat appears. This is hanging outside of my office in the elevator lobby. It's fun to point out to visitors. How does it work?

The trick lies in starting with 2 identical copies of static and inverting the static in one of the images in the area you want to appear black. That way, when the copies are aligned the regular static is still just static, 50% gray, but in the other area the black pixels are aligned with the clear pixels and vice versa, so that part is dark.

Note that inverted static holds as much information as non-inverted static, that is, zero. Neither of the sheets of static contain an image of the cat. It's only by juxtaposing the two images that the information can be generated/retrieved.

Skolelaboratoriet Logo

Skolelaboratoriet is a department that is housed on the same floor as Matematikksenteret where I work. My first day on the job I was pleased to see their logo:

 

Can you see what is special about it?

 

It show a dissection of a square into an equilateral triangle. The white piece in the middle stays in place and is common to both the square and equilateral triangle. The three upper pieces which are part of the square are moved below, each with a 180° rotation, to create the equilateral triangle on the bottom. I've never tried to work out the angles and lengths involved to accomplish such a dissection, but it looks like a nice little problem. I'll try to remember to think about this next time I have a long flight.

The dissection is even a little better than a simple cut-and-rearrange: the pieces can be hinged so that one form turns inside out to become the other.

George Hart presents a coffee table that performs this trick:

http://blog.makezine.com/2011/04/04/math-monday-mathematical-coffee-table/

Cobblestone scallops

These scallop patterns in the cobblestone in downtown Trondheim are interesting. If you were laying cobblestone, how would you determine the layout for these stones? Using your technique, what other interesting curvy designs are possible?

Lady in Glass

Peter Sutton is a glass artist in Trondheim, Norway. He and I collaborated on this project, a lady in glass:

 

I designed 23 cross-section slices which he printed on sheets of glass and assembled into an elegant block. The result is a 3d model floating in a solid chunk of glass. Here's a view of the cross-sections:

Extra second, and celebrating a gigasecond

Last night an extra second was added to world time. It happened at 23:59:60 UTC, or Universal Time which is the same as Greenwich Mean Time minus daylight savings. Here in Norway we're at GMT +1 which is UMT +2, so it happened just before 2:00 a.m. here.

I stayed up late to celebrate. It was an eerie feeling, to experience a minute go by that was 61 seconds long. It dragged on and on and on and we began to wonder when this minute would ever end. Whoa. Good thing they only happen every 4 years or so.

Reminds me of when I turned one billion seconds old. It happens sometime when you're 31 years and some months old. I remember thinking about it when I turned 31 and I calculated the date. It was 252 days away and I soon forgot about it.

One morning I got an email from a guy I hadn't from in 10 years. The email simply said "Happy Gigasecond!" I panicked! I'd forgotten! Was it today? Had I missed it? I furiously calculated. I was born in Indiana at 1:02 p.m., now I was in Washington, I had to account for time zone changes and daylight savings. I found out the exact second... and I still had 4 hours to go. I celebrated by popping open a malty beverage at the exact second while in my hot tub. It felt good to be aware of and celebrate the exact second.

But I still had a mystery – how did this guy know? I wrote him back to thank him. Turns out 10 or 15 years ago at a juggling club meeting we all figured out the exact dates we'd turn one billion seconds old. Dave L. had written down all of these dates in his calendar, and being a very organized person at the end of each year he would buy a new calendar and transfer all of the relevant information from the old calendar to the new. This he did again and again, and when it came to be my turn, he tracked down my email address.

Dave, you're my hero! If I'd missed it I would have needed to wait until 63 to celebrate the next one.

Burning calories

There was a discussion at lunch today about how eating a big chocolate bar can require 2 hours on an exercise bike to burn it off. I've always found these comparisons a bit misleading. It makes it sound like that's the only way to keep from getting fat.

Fact is, a 100 g of milk chocolate has about 520 calories, which will indeed take 1 to 1.5 hours to burn off on an exercise bike. Or you could just sleep for 7 or 8 hours and it would also be burned off.

So go ahead and have that candy bar! Just be ready to either cycle for 2 hours or sleep for 8 hours. OR... sleep for 10 hours and lose weight. Mmmm... chocolate + naps = weight loss. I think I could start a very popular weight loss program.