Asian Journal of Mathematics

Volume 26 (2022)

Number 5

Contact of circles with surfaces: Answers to a question of Montaldi

Pages: 613 – 616



Peter Giblin (Department of Mathematical Sciences, University of Liverpool, United Kingdom)

Graham Reeve (Department of Mathematics and Computing, Liverpool Hope University, Liverpool, United Kingdom)


We answer a question raised by J. Montaldi in 1986 as to the exact upper bound on the number of circles which can have $5$-point contact with a generic smooth surface $M$ in $\mathbb{R}^3$, at a point of $M$.


surface, circle, contact, roots of polynomials, distance-squared function, Euclidean, generic geometry, higher vertex

2010 Mathematics Subject Classification

53A05, 57R45, 58K05

Received 6 June 2022

Accepted 27 June 2022

Published 13 April 2023