5 papers
The unreasonable effectiveness of the cathetus rule in ancient and modern optics
Gavin R. Putland
The "cathetus rule" in optics alleges that the image of an object-point, formed by reflection or refraction at a surface, lies on the perpendicular ("cathetus") from the object-poi…
Obituary for Augustin Fresnel
Alphonse Duleau, Gavin R. Putland
Annotated English translation of Duleau's "Notice sur A. Fresnel" in Revue encyclopédique, vol.39, pp.558-67 (September 1828), and of the shorter obituary for Fresnel in id., vol.3…
Generalized Gregorian quadrature, including end-corrected weights for the midpoint rule
Gavin R. Putland
A class of numerical quadrature rules is derived, with equally-spaced nodes, and unit weights except at a few points at each end of the series, for which "corrections" (not using a…
Exact formulation of Huygens' principle in terms of generalized spatiotemporal-dipole secondary sources
Gavin R. Putland
A "spatiotemporal dipole" wave source, as defined by D.A.B. Miller (1991), differs from an ordinary ("spatial") dipole source in that the inverted monopole is delayed relative to t…
The cycloid as brachistochrone: A one-page proof, from first principles, without calculus
Gavin R. Putland
Johann Bernoulli's optical solution of the brachistochrone problem is rebuilt on underlying (non-optical) principles. An "optical interpretation" is given afterwards.