Jarnik

Jarnik (also spelled Jarník), may refer to:

• Vojtěch Jarník (1897-1970): A Czech mathematician noted for his contributions to number theory and mathematical analysis. His work includes research in Diophantine approximations, lattice point problems, and differential geometry. He is particularly well-known for Jarník's algorithm (see below) and Jarník's inequality.

• Jarník's Algorithm: An algorithm, independently discovered by Robert C. Prim, used to find a minimum spanning tree for a weighted, connected, undirected graph. It is also known as Prim's Algorithm. The algorithm iteratively adds the shortest possible edge from the connected component containing the starting vertex to another vertex outside of this component until all vertices are connected.

• Jarník's Inequality: A mathematical inequality relating the Hausdorff dimension of a fractal set to its packing dimension. It provides bounds on the size of sets related to Diophantine approximations. The inequality is named after Vojtěch Jarník.

• Jarník Limit: In the context of Diophantine approximation, the Jarník Limit concerns the approximation of irrational numbers by rational numbers. It provides a lower bound on how well an irrational number can be approximated by rational numbers with a given denominator.