I was flipping through Owen Jones’s Grammar of Ornament a couple months ago, and my eye was caught by this handsome pattern I had not noticed before. This is Jones’s Plate XLII, in the chapter on designs from the Alhambra in Granada, Spain. He calls it, “Part of the ceiling of the Portico of the Court of the Fish pond.” Since then I’ve kept out a clipboard with a compass and straightedge, and, in the small triangles of time after meals or before working on something else, I’ve slowly figured out how one might construct this. It’s less complicated than it looks at first, and at the same time ..read more

(This is the math geek part about the Sala de la Barca ceiling. For instructions on constructing the pattern with compass and straightedge, go over to Part 1.) In the process of figuring out how to draw this pattern, I ran into a lot of questions, and had to do more than a little math to answer them. Two families of symmetry One of the most interesting things to notice about this pattern is that it includes two distinctly different types of symmetry. There’s twelvefold symmetry inside the frame, but there’s eightfold symmetry on the frame. They’re not incompatible, but eightfold and twelvefold ..read more

Nord de Guerre Here’s a survey plat made in 1919 by a US Army unit in France. In the aftermath of WW1, teams of American military surveyors produced these as they went around France mapping the grave sites of fallen soldiers. On this plat we can see a number of bearings and distances from the I.P. (Initial Point), which is a small triangle at the centre of the image above. The bearing to the grave of Private Joseph A. Cain, for example, is “S 55°40′ W 598.5.” This means 55° 40′ west of due south — although we have to bear in mind that it was magnetic south, and specifically the magnetic sout ..read more

This story begins one day when I was assembling a map of the city of Edmonton, Alberta from OpenStreetMap data. It was going to be a big map, a 42″ (106 cm) wide poster for a wall. OpenStreetMap colour palette The data was good, but the standard OSM colours were not. They would work fine for a street map but, for a piece of art being seen all day in someone’s living space, there was an unpleasant amount of grey. Plus, the accents of pinky red and ochre, and the cold green parks, gave it a lack of colour harmony. If you analyze the colour profile of this map, counting the number of pixels of ea ..read more

Now that we know our way around the pattern (go back to Part 1), it should be fairly straightforward to construct with a compass and straightedge. But be aware: any pattern that requires you to construct a pentagon is an advanced challenge. They are trickier to make than squares or hexagons. Here’s what we want to draw: There are different scenarios for beginning. You might know where you want to site two rosette centres, and that will then determine the size of the master triangles and the rest of the layout. This is the scenario I’ll go through here. But, alternatively, you might want to sc ..read more

Just veering off into geometry here…. In November I was watching Eric Broug, an Islamic geometric design guru, give a talk online at an Islamic art conference, and I noticed that behind him they were projecting an interesting pattern on the scrim. I froze the video and grabbed a screenshot… What the heck is this? How do I look this pattern up? How do I find what pattern this is, and how to draw it? I have a few books of geometric patterns, but this was not in Eric Broug’s book Islamic Geometric Patterns, nor in Daud Sutton’s Islamic Design. So I took the tack of searching Jules Bourgoin, the ..read more

So, there I am, driving along in Edmonton, Alberta. I come to a stop light on Fort Road, look to my right and I see this: Is that a building with longitudes written on the roof?!?! And what are these longitudes? 9° 49’ W—that’s nowhere near Edmonton! Nor is 123°30’ E. What’s … going on here? A little sleuthing via Google Maps later revealed that this was the Kathleen Andrews Transit Garage. It’s owned by the Edmonton Transit Service, which operates all of the buses and light rail in the city. But the rooftop details were part of an art installation by Thorsten Goldberg called 53° 30′ N. Eac ..read more

The Maps for Books collection has a new page: Peter Erasmus’s Buffalo Days and Nights. The online maps of places described in Buffalo Days and Nights In 1920, Henry Thompson, an Alberta newspaperman, began interviewing 87-year-old Peter Erasmus, who lived near him in the area of Whitefish Lake, Alberta. Erasmus, who had been born in 1833 in the Red River settlement of what is now Manitoba, told him his life story, an account later published in book form by the Glenbow Institute as Buffalo Days and Nights, by Peter Erasmus as told to Henry Thompson. (It’s not an easy book to find in print. Yo ..read more

In a presentation I gave at GeoIgnite 2021, I was explaining the process of making shaded relief from DEMs (which I have a more detailed post on here). There wasn’t time to explain the process of re-projection, so instead I rather boldly asserted asserted that you don’t need to re-project your DEMs before making shaded relief. Instead, I said, you can just use the magic scaling number 111120 to convert from degrees to metres. Really? Is this true? Well, yes, in many cases it works pretty well. But, there are also some caveats. This technique fools with the terrain a bit, and could potentially ..read more

I’m wrapping up my work on Gottfried Merzbacher—a sort of back-burner project that’s been active and then dormant, on and off, for about seven years. It’s been a pleasure to learn about places like the Bayumkol valley, the relationship between the Saryzhaz and Kum-erik Rivers, and the placement of peaks around the head of the amazingly long Enylchek Glacier. This geography, while not unknown to residents of the Kyrgyz Republic or the Chinese province of Xinjiang, is downright obscure for North Americans—except perhaps among mountaineers and specialist geographers—so it’s been exotic and, durin ..read more