Peter M. Maurer
"A Rose is a Rose…", American Mathematical Monthly, 1987
American computer scientist whose 1987 article "A Rose is a Rose…" in the American Mathematical Monthly joined points on a rose curve with straight lines.
Maurer Rose
Hop round a rose curve in steps of the same angle and join the dots. One whole number for petals and one for the step make nets, stars and lace.
About this pattern
Peter Maurer, 1987 · Guido Grandi, 1723
The rose curve r = sin(nθ) was named by the Italian priest and mathematician Guido Grandi, who studied it in the 1720s: it has n petals when n is odd and 2n when n is even. In 1987 Peter Maurer, in an article in the American Mathematical Monthly called "A Rose is a Rose…", gave it a twist. Instead of tracing the curve, jump along it: go round in steps of d degrees, 360 steps in all, and join each point to the next with a straight line.
With d = 1 you just get the rose, drawn with straight segments. With most other steps the line zigzags from petal to petal and the drawing turns into a web, a star, a lace collar or a dense mesh, and steps a single degree apart can look nothing alike. Whatever the step, after 360 of them the pen is back where it started, so every Maurer rose with a whole-number step is a closed polygon.
Steps that share a factor with 360 close up sooner and draw fewer lines, which is why some steps look so sparse. The sheet shows a grid of them, petals increasing down the rows and the step across the columns, like a specimen book.
In motion the step drifts a fraction of a degree to each side, and the whole web shivers through its neighbours.
Behind the mathematics