3 papers
math.HO2025
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…
physics.optics2025
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…
physics.class-ph2025
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.