This artwork depicts a small sample of the infinite number of parabolas that pass through three points. It is based on a recent paper ("All Parabolas through Three Non-collinear Points" by Huddy and Jones; Mathematical Gazette 102, July 2018, 203-209). Three control points are rotated around the \(z\)-axis resulting in three rings. A parabola exists with an axis of symmetry at every angle \(\theta\) in the range 0 to \(\pi\) except the three where the line defined by a pair of the control points is parallel to the axis of symmetry of the corresponding parabola. The parabola with an axis of symmetry at an angle \(\theta\) is associated with a parabola in the sculpture in the \(xz\)-plane rotated around the \(z\)-axis by an angle twice \(\theta\).
Exhibition History
Exhibition of Mathematical Art,
Joint Mathematics Meetings, Denver, Colorado. 14–18 January 2020.
Press Coverage
References
- "All Parabolas through Three Non-collinear Points" by Huddy and Jones; Mathematical Gazette 102, July 2018, 203-209.