# La Maddalena and the non-Reuleaux table

I recently returned from a trip to Europe, with a one-day stopover in Rome, a visit to La Maddalena (a small resort island between Sardinia and Corsica) for FUN 2018, another stopover in Copenhagen, and a visit to Malmö, Sweden, for SWAT 2018. I’m still processing photos, but the first batch, from La Maddalena, is now up.

Despite being annoying to get to (an hour’s drive and another half-hour ferry ride from the nearest minor airport), La Maddalena is a very pleasant place to hold a conference, with a beautiful coastline and great food. The hotel was a little quirky (for instance, no potable water in the taps) and just enough inland to not have an ocean view, but it was still comfortable enough. Here’s what I could see from my hotel room:

You might notice the little triangular patio table on the balcony. Like several other kinds of rounded triangle, this is not a Reuleaux triangle, even if one ignores the rounded-off corners. On a Reuleaux triangle, the tangents to the two circular arcs that meet at a vertex would form \(120^\circ\) angles; here, the angle seems somewhat acute. And the distance from corner to corner is noticably larger than the distance from a corner to the middle of the opposite side. It’s clearer in a top view:

Notice how much more room there is on the top and bottom margins of the square frame than on the left and right. I’ve superimposed a circular triangle with right-angled corners (also not Reuleaux) to show that the sides of the table are even a little bit straighter than the superimposed triangle. I’m not sure whether they’re circular arcs or some other curve, but if they are circular I’d guess they span only about a \(20^\circ\) arc, compared to \(30^\circ\) for the superimposed triangle.

The rest of the gallery is less about furniture geometry and more about pretty views, so check it out. The one below is from the end of the conference excursion, a boat trip to some nearby islands.