Math in the News: 10/17/11

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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?

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Math in the News: 10/17/11

  1. 1. 10/17/11
  2. 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. 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. 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. 5. Scale Model of the Washington Monument Draw a horizontal line.
  6. 6. Scale Model of the Washington Monument Mark off a length of 55 units.
  7. 7. Scale Model of the Washington Monument Construct the perpendicular bisector of the 55-unit segment. Use the compass to construct the bisector.
  8. 8. Scale Model of the Washington Monument Mark the vertical height of 550 units.
  9. 9. Scale Model of the Washington Monument From the top point, mark a vertical length of 55.5 units.
  10. 10. Scale Model of the Washington Monument Construct the horizontal segment shown.
  11. 11. Scale Model of the Washington Monument Construct the horizontal segment shown.
  12. 12. Scale Model of the Washington Monument Create the outline of the monument.
  13. 13. Scale Model of the Washington Monument You now have a scale model of the Washington Monument.
  14. 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. 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. 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. 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.”

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