Between 1971-1975, Halaby shifted away from ‘the confines of the rectangle’ and explored her ‘Helixes and Cycloids’ series. This revelation came after painting a portrait of Nabil-al Nawaab, an Iraqi she befriended while teaching in Indiana, when she noticed she had incorporated geometric experimentations as a still life within the portrait. These new paintings repositioned her focus, articulating these inherent motions to proceed diagonally onto the canvas.

Halaby focused on helical and cycloid curves, extending time into drafting helix curves from her study of books on geometry used by engineers specialising in cutting and fitting heating pipes, and selecting a rectangular section for a painting. She bent strips of aluminum and steel, copying their reflective colours and narrow bands of colour that fade into each other, as would appear in both works. In these paintings, it is indistinguishable to differentiate between foreground and background; instead of defining her composition within a two-dimensional plane, she creates a ‘continuum between volume and surface’ identified in Islamic art and architecture in the mid-1960s. Fascinated with the illusions of distant horizons and our ability to articulate the invisible line between a curved surface and the distance behind it, Halaby explores the boundaries of her practice.