Tricurves were introduced to the Aperiodical audience via Tim Lexen‘s posts Bending the Law of Sines, Combining Tricurves, Phantom Tiling, and (joint with Katie Steckles) Making Tricurves. Like Tim and Katie in that last post, when introduced to a new concept I like to play around with it to see it from different perspectives. Tiling…

# Search Results for: tricurves

### Making Tricurves

Tim Lexen has written a series of posts on the topic of Tricurves: Bending the Law of Sines, Combining Tricurves and Phantom Tiling. In this latest post, Tim has been working with our own Katie Steckles to turn Tricurves into real objects to play with. When you discover an interesting mathematical shape or object, there’s a…

### Combining Tricurves

In July, guest author Tim Lexen wrote about his discovery of the tricurve, a shape made of arcs that has some interesting properties. He’s written a follow-up in which he explores them further. For a discussion of tiling with curve-sided shapes in general, see Tim’s MathBlog post. Tricurves can be combined when the large, convex arc of one…

### Small Sets of Arc-Sided Tiles

Tim has previously written guest posts here about tiling by tricurves, and is now looking at ways of tiling with other shapes. In an earlier post elsewhere I covered some basic arc-sided shapes that tile by themselves. Lately I’ve been playing with groups of curved tiling shapes, asking a question common for me: how to…

### Phantom Tiling

Following on from his previous posts: Bending the Law of Sines, which introduced the idea of tricurves, and a further post on Combining Tricurves, Tim Lexen continues this series of guest posts by looking at some of the structures underlying tricurve tilings. When we look at simple planar shapes for tiling, usually each shape’s properties and…

### Bending the Law of Sines

For me, the above shape emerged when playing with a drawing compass. Of the two ancient tools, I preferred the compass over the straightedge. I was fascinated with the classical geometric constructions, the intersecting circles and arcs. As a simple personality test, preferring a compass over a straightedge might mean something: maybe roundabout-holistic-intuitive more…