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

1. 11/14/11

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. 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. Statue of Liberty
• Bartholdi’s innovative
design would achieve
the grandeur of the
Colossus, while still
creating a relatively
light, sturdy structure.

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. 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. 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. 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. 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. Statue of Liberty
The copper used has a mass of 27,220 kg and it is 2.4 mm thick, about the
thickness of two pennies.

11. Statue of Liberty
If 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. Statue of Liberty
We know the height of the sheet, but how can we find the surface area of the
sheet? For that we need to work with the density of copper.

13. Statue of Liberty
The surface area (or the product of L and W) is found by dividing the mass of the
copper sheet by the product of the density and H.

14. Statue of Liberty
We know the values for the density of copper, the mass of the copper used to
construct the Statue of Liberty, and the height H.

15. Statue of Liberty
Input 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 units
consistent.

16. Statue of Liberty
Use these formulas to convert grams to kg, cm to meters, and mm to meters.

17. Statue of Liberty
This equation makes the needed adjustments so that all mass units are in kg and
all distance units are in meters. The surface area is 1268.64 square meters,
equivalent to a 40-yd by 40-yd area.

18. Statue of Liberty
But the actual surface area is larger, since the copper sheets were hammered into
a larger shape.

19. Statue of Liberty
Here’s an example. Suppose you hammer a square sheet so that it is half a
cylinder wide. Based on the dimensions shown, this results in a 57% increase in
the surface area, which is a huge increase.

20. Statue of Liberty
In the case of the Statue of Liberty the copper sheet conforms to a much wider
circle.

21. Statue of Liberty
The width of this great circle is based on the width of the Statue of Liberty. Let’s
assume each copper sheet is a 1 mx 1 m square. The surface is based on the
width of the copper sheet, the angle it forms, and the radius of the great circle.

22. Statue of Liberty
Using the the known measurements we can find the measure of the angle in
radians. This results in a nearly 100% increase in the surface area!

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. Statue of Liberty
The New Colossus
Not like the brazen giant of Greek fame,
With conquering limbs astride from land to land;
Here at our sea-washed, sunset gates shall stand
A mighty woman with a torch, whose flame
Is the imprisoned lightning, and her name
Mother of Exiles. From her beacon-hand
Glows world-wide welcome; her mild eyes command
The air-bridged harbor that twin cities frame.
"Keep, ancient lands, your storied pomp!" cries she
With 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