Vincenty's Formulae are two methods named after Thaddeus Vincenty a Polish-American geodesist who lived during the 20th Century. During his career, he devised his formulae as well as contributing to major projects such as the NAD 83 where he introduced three-dimensional Earth-centered coordinates. Vincenty's formulae were published in 1975 and it can be downloaded and read here.
The formulae were developed for calculating geodesic distances between a pair of latitude/longitude points on an ellipsoidal model of the Earth (an oblate sphere). This ellipsoidal geometry is the next step, and perhaps, more appropriate geometry to use when modeling the Earth from working with a sphere using the Haversine Formula see
