Architecture has an obvious and visible link with geometry. Clear lines, rectangular or triangular shapes have dominated for centuries since the Greek temples. Geometry was a discipline that has attracted many scholars and particularly architects. Nowadays the shapes are much more diversified and sometimes complex. The calculation of surfaces, curved lines and shapes have become an issue of more complicated mathematics. Volumes of irregular shapes are a challenge for most people to calculate and heating or cooling sich buildings adds considerable complexity. It is, however, rather relaxing and fascinating to look at the marvels of modern shapes in architecture. Technology and material science have allowed us spectacular progress and designs in recent years. Paris offers a splendid perspective on such developments.