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# Math in the News: 11/14/11

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In this episode of Math in the News we look at the geometry and architecture of the Statue of Liberty.

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### Math in the News: 11/14/11

1. 1. 11/14/11
2. 2. Statue of Liberty• The Statue of Liberty was a gift from the French to the U.S. and it was designed by Frederic- AugusteBartholdi.
3. 3. Statue of Liberty• Bartholdi wanted to create the effect of the Colossus of Rhodes, one of the ancient wonders of the world. It was a massive stone statue that, unfortunately, collapsed over time due to an earthquake.
4. 4. Statue of Liberty• Bartholdi’s innovative design would achieve the grandeur of the Colossus, while still creating a relatively light, sturdy structure.
5. 5. Statue of Liberty• The Statue of Liberty is an example of a curtain wall structure. It has a solid framework upon which a “curtain” of copper sheets were hammered and riveted in place.
6. 6. Statue of Liberty• The simplest example of a curtain wall structure is a tent. The metal framework keeps the structure intact and acts like a skeleton for the tent. The walls are made of fabric that is tightly connected to the framework.
7. 7. Statue of Liberty• Gustav Eiffel, famous for the Eiffel Tower, constructed the framework for the Statue of Liberty. His work was extremely important, since the Statue of Liberty faces strong winds and needed a sturdy but somewhat flexible structure.
8. 8. Statue of Liberty• Upon this framework, sheets of copper were hammered into the shape of the Statue. The hammering was done from the inside of the statue outward.
9. 9. Statue of Liberty• We know the amount of copper used in the Statue, and we know the thickness of the copper, but how can we calculate the surface area of the copper used, and therefore the surface area of the Statue itself?
10. 10. Statue of LibertyThe copper used has a mass of 27,220 kg and it is 2.4 mm thick, about thethickness of two pennies.
11. 11. Statue of LibertyIf you think of the copper used as a flat sheet, then it has dimensions L (for length),W (for width), and H (for height).
12. 12. Statue of LibertyWe know the height of the sheet, but how can we find the surface area of thesheet? For that we need to work with the density of copper.
13. 13. Statue of LibertyThe surface area (or the product of L and W) is found by dividing the mass of thecopper sheet by the product of the density and H.
14. 14. Statue of LibertyWe know the values for the density of copper, the mass of the copper used toconstruct the Statue of Liberty, and the height H.
15. 15. Statue of LibertyInput the values in the surface area equation. Note that there is a mixture of units(kg and g for mass and cm and mm for length). We need to make the unitsconsistent.
16. 16. Statue of LibertyUse these formulas to convert grams to kg, cm to meters, and mm to meters.
17. 17. Statue of LibertyThis equation makes the needed adjustments so that all mass units are in kg andall distance units are in meters. The surface area is 1268.64 square meters,equivalent to a 40-yd by 40-yd area.
18. 18. Statue of LibertyBut the actual surface area is larger, since the copper sheets were hammered intoa larger shape.
19. 19. Statue of LibertyHere’s an example. Suppose you hammer a square sheet so that it is half acylinder wide. Based on the dimensions shown, this results in a 57% increase inthe surface area, which is a huge increase.
20. 20. Statue of LibertyIn the case of the Statue of Liberty the copper sheet conforms to a much widercircle.
21. 21. Statue of LibertyThe width of this great circle is based on the width of the Statue of Liberty. Let’sassume each copper sheet is a 1 mx 1 m square. The surface is based on thewidth of the copper sheet, the angle it forms, and the radius of the great circle.
22. 22. Statue of LibertyUsing the the known measurements we can find the measure of the angle inradians. This results in a nearly 100% increase in the surface area!
23. 23. Statue of Liberty• This near-doubling of the surface area of the statue results in a much more massive structure without any increase in the weight of the statue. The Statue of Liberty looks massive but has a relatively light footprint.
24. 24. Statue of Liberty The New ColossusNot like the brazen giant of Greek fame,With conquering limbs astride from land to land;Here at our sea-washed, sunset gates shall standA mighty woman with a torch, whose flameIs the imprisoned lightning, and her nameMother of Exiles. From her beacon-handGlows world-wide welcome; her mild eyes commandThe air-bridged harbor that twin cities frame."Keep, ancient lands, your storied pomp!" cries sheWith silent lips. "Give me your tired, your poor,Your huddled masses yearning to breathe free,The wretched refuse of your teeming shore.Send these, the homeless, tempest-tost to me,I lift my lamp beside the golden door!" Emma Lazarus, 1883
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