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# Parabolas of the Eiffel Tower

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## Olivia Thompson

on 13 April 2014

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#### Transcript of Parabolas of the Eiffel Tower

Setting Up
If the top of the arch is 57 meters, and two base legs are 66 meters apart, we can make our three points: (0,57) (33,0) (-33,0). We are going to use standard form to set up our matrices: y=ax^2+bx+c. You substitute in all three points, three times to make:
57=a(0)^2+b(0)+c
0=a(33)^2+b(33)+c
0=a(-33)^2+b(-33)+c
Now you can set up three matrices to solve this system.
Solving with Matrices
History
The Eiffel Tower was originally built for the Universal Exhibition in Paris and it was almost torn down in 1909 but it was saved because of its telegraphy functions.
Upkeep
50-60 tons of paint are added to the tower every 7 years to keep it from rusting.
Matrices
0 0 1 a 57
33 33 1 x b = 0
-33 -33 1 c 0
Take the inverse of the first matrix and multiply both sides by the inverse of 1. But it's impossible because the determinant of the first matrix is zero, so the inverse does not exist.
System of Equations
Since the matrices didn't work, you now have to go back to the first three original equations we had and use combinations or substitution to solve.
The Eiffel Tower was named after Gustave Eiffel a.k.a "Magician of Iron". Built in 1889, it is 320 meters high, the same as a 105-story building. The weight of the iron structure is 7,300 metric-tons, but if it were a 30 cm model, it would only weigh 7 grams. There are 3 levels: first-57m-19 stories, second-115m-38 stories, and third-273m-89 stories. The base of the Eiffel Tower covers 100 square meters.

Dimensions
The base consists of four congruent legs, and they arch up to meet just under the first floor. The parabola's equation will be easy to find.
Relation to Algebra II
Parabolas of the Eiffel Tower
Combinations
Solving for a
More Combinations
Solve for b
Final Steps
Bibliography
"Eiffel Tower." > ENGINEERING.com. N.p., 13 Oct. 2006. Web. 13 Apr. 2014. <http://www.engineering.com/Library/ArticlesPage/tabid/85/ArticleID/62/Eiffel-Tower.aspx>.
"Eiffel Tower." Wikipedia. Wikimedia Foundation, 4 Dec. 2014. Web. 12 Apr. 2014. <http://en.wikipedia.org/wiki/Eiffel_Tower>