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 $$\theta$$.

### 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.