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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, however, as experienced bridge builders, 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.
The shape of the tower was determined by empirical methods accounting for the effects of wind, and graphical methods, without an overall mathematical framework. Careful examination of the tower shows a basically exponential shape; actually two different exponentials, the lower section overdesigned to ensure resistance to wind forces.

Several explanations have been proposed over the years; the most recent is a nonlinear integral equation based on counterbalancing the wind pressure on any point on the tower with the tension between the construction elements at that point. The tower sways 6–7 cm (2–3 in) in the wind.