The haversine function provides superior numerical accuracy for solving large triangles on Earth's surface compared to the spherical law of cosines, particularly when using limited-precision arithmetic. Historically used by navigators, the haversine method avoids precision loss from adding numbers of vastly different magnitudes and is more computationally efficient.
The article explores how Nathaniel Bowditch might have taught navigation to sailors who could only add and subtract by using lookup tables of logarithms and trigonometric functions. While theoretically possible, the scheme would require extensive tables and careful algorithm design to minimize the mathematical sophistication needed.