The Geometry in the Eiffel Tower
As you can see, the Eiffel Tower is very similar to the geometric shape of a four sided pyramid. At the base, there are four large semi circles, one on each side of the tower. Throughout the structure, there are hundreds of triangles and parallelograms seen in the intricate lattice work. The railings also form perfect rectangles.
The curvature of the tower's legs are mathematically determined to offer the most efficient wind resistance possible. Eiffel explains, "All the cutting force of the wind passes into the interior of the leading edge uprights. Lines drawn tangential to each upright with the point of each tangent at the same height, will always intersect at a second point, which is exactly the point through which passes the flow resultant from the action of the wind on that part of the tower support situated above the two points in question. Before coming together at the high pinnacle, the uprights appear to burst out of the ground, and in a way to be shaped by the action of the wind."
While building the Eiffel Tower, the constructors and workers had to be as precise as possible. The 18,000 pieces used to build the tower was carefully designed and calculated to the accuracy of a tenth of a millimeter. These pieces were then put together to form the four base pillars. The pillars had to be placed 80 meters apart and hand to be propped up with millimeter precision fifty meters above the ground. The pillars are oriented in the manner of the four cardinal points, contained within a square with 125-meter sides.
The triangular design of the Eiffel Tower gives the tower strength from the rigidity of the triangular shape. A rectangle fromed by four bars joined at their ends can be flattened into a parallelogram, but the triangel cannot be in any way deformed except by bending or stretching the bars. Thus, the Eiffel Tower's frame is composed of a web of triangles.
The force of the wind causes the top of the Eiffel Tower to sway 6 to 7cm.
Heat also causes the Tower top to move, with a curve of movement measuring 18cm.
The Eiffel Tower has to be repainted every 5 years, using 50 tons of paint.