Listen With Others

I don’t remember where I first read about the Bézier curve, but it rang bells as an ideal construction for a crossword. All that was needed was some logic for the lines, and linking identical cells seemed to be appropriate. I had the option of using horizontal and vertical locations, but figured I could hide the theme better if I used a diagonal. It also resulted in a more pleasing curve.

I needed to avoid any duplicate letters in each location, and also had to accommodate clashes. I started with the bottom row, which forced the letters along the diagonal, then tackled each clash in turn, which drove most of the bar locations. I was lucky to find the 11-letter words, as these helped boost the average entry length.

I tried to make the clues moderately challenging, as there were many over-checked entries, particularly in the NW corner, where there were no clashes. My favourite was  4 Down, Having uncovered nostrils, restored lung harmony (11), as it gave a good surface reading for a real stinker of a word. This clue made it past the vetters unscathed, but some were amended, largely for concision.

I’ve seen feedback from solvers who thought it was unnecessary to include the computer applications. I’m generally not a fan of additional twiddles myself, but I was keen to add something here to highlight the curve’s practical significance. If you’ve ever appreciated the beauty of car body shapes, or indeed anything manufactured during the computer era, then thanks are in no small part due to Pierre Bézier, who helped develop the automated design and manufacturing tools and techniques during his 40 years working for Renault. He was not the first to discover this curve, however. He independently created an algorithm first devised by Paul de Casteljau, who worked at Citroën. Bézier died in 1999 at the age of 89, and de Casteljau died in March 2022, at 91 years.

To me, the Listener Crossword is all about revealing a theme of interest. Without its practical applications, the Bézier curve, like many other topics in pure mathematics, would be little more than a pretty abstraction.

Both vetters mentioned that the construction reminded them of string art from the 1970s. Although aware of the toy, I hadn’t really considered this in the context of the puzzle, and in retrospect, I could have hinted at it somewhere. One vetter also remarked that all those lines might make it difficult for the marker to check the letters underneath. I hope everyone left their letters legible, otherwise I’ll have to change my setter name to Mud.