In this issue of Math in the News, we look at the geometry and architecture of the Washington Monument, in light of the recent earthquake. Why did the Washington Monument sustain so much damage?

1. 10/17/11

2. Washington Monument
• On August 23, 2011,
an earthquake of
magnitude 5.8 struck
Virginia. The epicenter
of the earthquake was
over 80 miles from
Washington, DC.
• Yet, the Washington
Monument sustained a
good deal of damage.

3. Washington Monument
• This link includes a
number of videos
showing the interior
and exterior of the
Monument during the
earthquake. Note the
extensive amount of
damage to the interior.
• http://www.nps.gov/wamo/

4. Washington Monument
• Why would the
Washington Monument
be so affected by the
earthquake, while most
buildings were not?
• Let’s investigate the
geometry of the
Monument using
paper, pencil,
straightedge, and
compass.

5. Scale Model of the Washington Monument
Draw a horizontal line.

6. Scale Model of the Washington Monument
Mark off a length of 55 units.

7. Scale Model of the Washington Monument
Construct the perpendicular bisector of the 55-unit
segment. Use the compass to construct the
bisector.

8. Scale Model of the Washington Monument
Mark the vertical height of 550 units.

9. Scale Model of the Washington Monument
From the top point, mark a vertical length of 55.5
units.

10. Scale Model of the Washington Monument
Construct the horizontal segment shown.

11. Scale Model of the Washington Monument
Construct the horizontal segment shown.

12. Scale Model of the Washington Monument
Create the outline of the monument.

13. Scale Model of the Washington Monument
You now have a scale model of the Washington
Monument.

14. Washington Monument
• The shaking from the
earthquake makes the
whole monument
vibrate, but the
strongest impact is felt
at the monument’s
center of gravity.

15. Scale Model of the Washington Monument
Because the Monument has vertical symmetry, you
can easily locate the center of gravity by connecting
the midpoints of the vertical sides.

16. Washington Monument
• The Washington
Monument was not
designed to withstand
earthquakes. Given
that it is a rigid stone
structure, even minor
vibrations will create
cracks in the stone.
• We would expect more
damage near the
center of gravity.

17. Washington Monument
• Watch the helmet cam
video of the workers
rappelling the side of
the Monument. Note
where the cracks are
located.
• http://www.nps.gov/wamo/
• Click on “Helmet Cam.”