Category Archives: Math

Maps not to be Taken Literally

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Flickr: Eisenhower Interstate System in the style of H.C. Beck’s London Underground Diagram

At least this map isn’t quite as distorted as the DC metro map, but I see e.g. it has Schenectady closer to Syracuse than Albany, and the route from Albany to Boston as a straight line, as one should expect of a schematic map, where your lines are limited to the eight choices at 45º

I’ve long despised the DC Metro map, because it was useless to me the first time I needed to get around while visiting; the cabbies were on strike, and I was forced to use plan B, except I had no plan B at the time. The schematic layout made little sense to me as I wasn’t familiar with the geographical layout of the city.

See Beck’s Tube Maps

Wait! That's Not All!

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Rhett’s got a post up on parallax, and how you can use this effect to measure distance: Parallax, what is it good for? He’s got some pictures showing the effect of viewing from different vantage points.

The other thing you can do with such photos is to make stereograms, and I’ve taken the liberty of doing so with Rhett’s image, though I didn’t try and take out the dotted lines.

Rhettparallax

Cross your eyes and you can make the image take on depth. In case you want more, here’s the optics layout stereogram I posted a while back.

Name that Fractal

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sevensixfive: Circles

This is an open question: What is this fractal? It’s a method for filling a 2D plane with circles in an orderly way – circles made of circles, all the way down. There are published examples of similar systems, like the Apollonian Gasket, the Kleinian Groups, Indra’s Pearls, but I’ve never seen this particular arrangement before, and I’ve been looking for over ten years. Is this a trivial variation on something already known? Or a new and undiscovered thing? I have no idea. I found it while doodling in math class.

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Update: It’s an “orbit of a circle under a Kleinian group generated by two Mobius transformations (one elliptic of order 4, one parabolic)” explanation (PDF)