Antoni Gaudi was a Catalan architect whose career seemed to have consisted of one masterpiece after another, with his most famous masterpiece being his Sagrada Familia in Barcelona. The Sagrada Familia (“Sacred Family) is a church which is essentially dedicated to the life of Christ. When I visited the church in the summer of 2022, I noticed that the inside of the church seemed almost like a dedication to math and nature. After taking Math 201 I now had some of the skills to describe the geometry I saw. Built in the shape of a cross, the giant nave is held up by large columns which are obviously modeled after trees and described as hyperboloids (of one sheet). The base of the columns have a larger radius which gets smaller as the columns get taller. The column then splits into branches towards the top which once again expands its radius. Surrounding each column are four images of archangels displayed right before the columns branch off. Each of these images are set on ellipsoids embedded into a larger ellipsoid which surrounds each column!
The tree-like columns all lean slightly towards the center of the gorgeous ceiling, full of geometric designs. This helped me recognize the shape of the ceiling as a saddle, or hyperbolic paraboloid, a shape that we spent a lot of time analyzing in class. The columns lean in to meet the ceiling where the saddle dips down. The final shape I observed in the Sagrada Familia was the helicoidal shape of the stairs. I utilized my knowledge of graphing parametrically to figure out how to model the helicoid. As humans we are drawn to look at things with some sort of pattern or symmetry, even if we don’t know what it is. At the Sagrada Familia, you are drawn to look at everything.
