More Experimental Topology and Experiments in Topology

I visited my friends Peter and Liz (I stayed a few nights) and came back with a laundry list of things to post about:

1) They have some really cool polyhedra and mathematical quilts, so sometime I am going to have to go over there with a camera and click some photos. Peter’s latest quilt project is one tiled with spidrons, which is in the design phase now.

2) Peter was a little upset that I failed to credit him for pointing out to me originally that 7\times 3=21 and 7 expanded base 3 is 21 (see synchronicity) and asked if there were any other examples of this. Anyway, thanks, Peter, for pointing this out and inspiring so much recreational math.

3) I finally carried out that idea I had that I mentioned back in the post more experimental topology about making a five pointed star. It took some trial and error (hey! that’s what experimental topology is all about. Right?) but here is what I came up with:

Start with ten strips of paper, with one end cut into points. The points should come to an angle of approximately \frac{\pi}{5}.

Draw a line down the center of each and tape them together so that the tips are all touching:

Now start taping opposite ends together, like so:

When you have four of the five opposite pairs taped together, the last one needs one full twist. If you’ve been proceeding in a clockwise direction when taping opposite pairs together, you should make one full twist in the last pair by turning the strip closest to you in a counter-clockwise direction. Anyway, in the end you should get something like this:

Now, cut along all of those center lines, and what do you get?

A mess, but if you untangle the mess, you should get:

A pair of stars that are linked!

Topologically this is the Hopf link.

4) Peter also loaned me a couple of books:

Experiments in Topology

I haven’t read much yet, but it has some cool stuff, like if you have a strip of paper, one inch thick, what is the shortest Moebius strip that you could make?

Also he lent me

Goedel, Escher, Bach: an Eternal Golden Braid

(gosh, that’s a really small image of the book, but, oh well). I’m about a fifth of the way into this book. Excellent so far. Won the Pulitzer Prize! I’m learning lots about the works of Goedel, Escher and (believe it or not) Bach.

That’s all for now, but soon I will have to blog about my visit to my kids’ classes for career day, which was last week….Stay tuned.

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2 Responses to More Experimental Topology and Experiments in Topology

  1. Pingback: Topology: Have Fun With Geometry | Homeschool Library of Links

  2. climbert8 says:

    Great, just discovered your blog. I’ve been doing math play as well with my kids (and some years back ran a club middle school kids). I just bought “experimental topology” a few days ago, and had read GEB in college.

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