Rigge Envelopes as Art Inspiration

John Sharp
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 171–178


Many artists using mathematical curves to generate lines in their work use Lissajous figures or cycloids. The mathematician William Rigge introduced a new technique in a paper in the American Mathematical Monthly in 1920 which he called envelope rosettes. In this paper, I look at what he was doing and develop some art which takes his ideas in other directions.