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Shape of the eiffel tower

At the time the tower was built many people were shocked by its daring shape. Eiffel was criticised for the design and accused of trying to create something artistic, or inartistic according to the viewer, without regard to engineering. Eiffel and his engineers, as renowned bridge builders however, understood the importance of wind forces and knew that if they were going to build the tallest structure in the world they had to be certain it would withstand the wind. In an interview reported in the newspaper Le Temps, Eiffel said:
“ Now to what phenomenon did I give primary concern in designing the Tower? It was wind resistance. Well then! I hold that the curvature of the monument's four outer edges, which is as mathematical calculation dictated it should be (...) will give a great impression of strength and beauty, for it will reveal to the eyes of the observer the boldness of the design as a whole. ”

—translated from the French newspaper Le Temps of 14 February 1887[11]

The shape of the tower was therefore determined by mathematical calculation involving wind resistance. Several theories of this mathematical calculation have been proposed over the years, the most recent is a nonlinear integral differential equation based on counterbalancing the wind pressure on any point on the tower with the tension between the construction elements at that point. That shape is exponential. A careful plot of the tower curvature however, reveals two different exponentials, the lower section having a stronger resistance to wind forces.[12][13]

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