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Architects need to be familiar with a wide range of technologies, methodologies, understand the software lifecycle, have design experience, and some say an architect must write code, and so on and so forth. Indeed, the hard skills are important, very important. However it doesn't stop there.
Architects and engineers must not only understand the basic principles and ideas behind geometry, they must also have a more in-depth understanding of the theorems and rationales which support geometry. These concepts are essential to ensure that buildings are structurally sound and able to withstand the forces of nature.