Parabolas
3D Printed Plastic, 10 in
2019

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 a pair of the control points are co-linear. 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.

### Publication History

- 2020 Joint Mathematical Meetings Exhibition of Mathematical Art, p. 76, Edited by Robert Fathauer and Nathan Selikoff, ISBN: 978-1-938664-33-5, Tessellations Publishing, 2020.

### References

- "All Parabolas through Three Non-collinear Points" by Huddy and Jones; Mathematical Gazette 102, July 2018, 203-209.