Kunstweg

The Kunstweg is a collection of mathematical procedures for calculating sine values to high precision, developed by the Swiss mathematician and instrument maker Jost Bürgi in the late sixteenth century and explained in his manuscript Fundamentum Astronomiae, presented to Emperor Rudolf II in 1592. Bürgi used the method to produce a canon sinuum, a sine table with entries every two arcseconds and accurate to eight sexagesimal places, which Johannes Kepler later praised as the most precise sine table known at the time and which was valuable for maritime navigation. The procedure works iteratively: each cell of a table is formed from the sum of the two preceding cells in its column, the final cell of each round is halved, and the process repeats until the values in the last column converge to an accurate sine approximation after only a few iterations.