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# The Eiffel Tower

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## L S

on 4 December 2013

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#### Transcript of The Eiffel Tower

The Tower
How does it relate to geometry?
Let's see!
The Shape
The tower is very similar to the shape of a four-sided pyramid
As you can see, at the base there are four large semi-circles
The railings at each level are perfect rectangles
There are also hundreds of triangles, parallelograms, and other shapes woven throughout the latticework
The Tower's Legs
The tower's legs are mathematically designed for the most efficient wind resistance possible
"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." -Gustave Eiffel
The Triangular Shape
The triangular design of the tower gives it strength from the rigidity of the triangular shape
A rectangle could be flattened into a parallelogram, but a triangle can not be deformed in any way except by stretching the bars
So, the tower was composed of a web of triangles
Building the Eiffel Tower
While building the Eiffel Tower, the constructors and workers had to be as precise as possible
Each of the 18,000 pieces used to create the tower were carefully designed and calculated to the accuracy of a tenth of a millimeter
The four base pillars had to be propped up with millimeter precision fifty meters above the ground
Other Ways
Everything in the tower is symmetric
Triangles, parallelograms, and many other shapes can be found all throughout the latticework
Tessellations can also be found in the latticework
FUN FACT!
The wind causes the tip of the tower to sway-- around 6 to 7 centimeters
FUN FACT!
Heat also causes the Tower top to move, with a curve of movement measuring up to 18cm.
FUN FACT!
The Tower has to be repainted every 5 years, using 50 tons of paint each time.
FUN FACT!
The Eiffel tower was the tallest manmade structure until the Chrysler Building was built in New York in 1930.
SOURCES:
Eiffel Tower: Information and Facts
http://www.livescience.com/29391-eiffel-tower.html
The Eiffel Tower- The Geometry in the Eiffel Tower
http://www.angelfire.com/hi5/eiffeltower/4Geometry.html
The Eiffel Tower- The Construction of the Eiffel Tower
http://www.angelfire.com/hi5/eiffeltower/3Construction.html
Eiffel
Full transcript