Professor Knuth presents his Annual Christmas Tree Lecture, "Planar Graphs and Ternary Trees." In this lecture, Professor Knuth discusses the beautiful .

the circle packing theorem describes the possible tangency relations between circles in the plane whose interiors are disjoint. for every connected simple planar graph G there is a circle packing in the plane whose intersection graph is G

Graph Creator: Use this vertex-edge tool to create graphs and explore them. Investigate ideas such as planar graphs, complete graphs, minimum-cost spanning trees, and Euler and Hamiltonian paths.

Example of PMFG, a maximally filtered planar graph with vertices 300 stocks, selected among ordinary common shares listed in the American Stock Exchange market and edges associated with the structure of strongest correlations between stocks (in the time period from 1981 to 2010).