The golden ratio—phi, or approximately 1.618—is the point at which two unequal parts of a line relate to each other in the same proportion as the whole line relates to the larger part. Euclid recorded it around 300 BCE. The Fibonacci sequence converges on it. Renaissance masters worked with it. Le Corbusier built an entire system of architectural proportion around it. What makes phi unusual as a basis for beauty is that it requires no prior knowledge from the observer. The eye recognizes the proportion as right, without being able to say why. That feeling of inevitability in the absence of explanation is, arguably, as precise a definition of beauty as we have. In 1968, Patek Philippe translated this principle into a watch case. The Golden Ellipse, the manufacture's first entirely new collection since the Calatrava of 1932, was conceived by Jean-Daniel Rubeli, then Patek's head of design, who had..