Montreal Olympic Stadium and surrounding structures, are but a few notable examples of the city's 20th-century architecture. Pavilions designed for the 1967 International and Universal Exposition, popularly known as Expo 67, featured a wide range of architectural designs. Though most pavilions were temporary structures, several have become landmarks, including Buckminster Fuller's geodesic dome U.S. Pavilion, now the Montreal Biosphere, and Moshe Safdie's striking Habitat 67 apartment complex. The Montreal Metro has public artwork by some of the biggest names in Quebec culture. In 2006 Montreal was named a UNESCO City of Design, only one of three design capitals of the world
Solving the geodesic equations curve γ("s") in formula_1 and formula_5 are the Christoffel symbols. The Christoffel symbols are functions of the metric and are given by: where the comma indicates a partial derivative with respect to the coordinates: As the manifold has dimension formula_8, the geodesic equations are a system of formula_8 ordinary differential equations for the formula_8 coordinate variables. Thus, allied with initial conditions, the system can, according to the Picard–Lindelöf theorem, be solved. One can also use a Lagrangian approach to the problem: defining and applying the Euler–Lagrange equation. As the laws of physics can be written in any coordinate system, it