## Nickalls' TheoremIf tangents from two points
This beautiful theorem crystalized from experimental observations in 1986 by Dick Nickalls (retired) from the Dept. of Anaesthesia, Nottingham University Hospitals, UK in the area of vision physiology - a rich source of mathematical problems. It relates to the so-called
- Nickalls, R.W.D. (2000). A conic theorem generalised: directed angles and applications.
*The Mathematical Gazette*, 84 (July), 232–241.*(Download).* - Rigby, J.F (2002). A proof of Nickalls' theorem on tangents and foci.
*The Mathematical Gazette*, 86 (July), 322-324.*(Download).*
Please WAIT while the applet loads. Drag points Click on hyperbola or parabola to dynamically interact with and investigate these other two cases of Nickalls' theorem. The theorem is also useful in providing easy proofs for other fundamental properties of conics such as "The circumcircle of the triangle formed by any three tangents to a parabola passes through the focus" (e.g. see Parabola Circumcircle Theorem), "The locus of the foot of the perpendicular from the focus of a parabola to a tangent is the tangent at the apex" (e.g. see Parabola Locus Theorem), etc. Michael de Villiers, updated 16 March 2012, created with GeoGebra |