Math in the News: Issue 53
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Math in the News: Issue 53

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In this issue of Math in the News we analyze the sinking of the Titanic. It has been a hundred years, yet the story of the sinkin g of the Titanic still fascinates. For more math media resources, go ...

In this issue of Math in the News we analyze the sinking of the Titanic. It has been a hundred years, yet the story of the sinkin g of the Titanic still fascinates. For more math media resources, go to http://www.media4math.com.

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Math in the News: Issue 53 Math in the News: Issue 53 Presentation Transcript

  • Why the Titanic SankThe Titanic was a British ship that set sail on April 10, 1912. It made twostops before heading toward New York. It never made it there. It sank onApril 15 after hitting an ice berg.
  • What happened to the Titanic? Click on this video to see the sequence of events that led to the sinking of the Titanic. http://youtu.be/qCv1jKHfFiY
  • Where is the Titanic now?Click on this video to see footage of the wreck of the Titanic. http://youtu.be/6Z7REEnwKOQ
  • Why the Titanic SankTo get a sense of how massive the Titanic was, this illustration gives anidea of the scale of the ship.
  • Why the Titanic SankThe key to sailing a ship of this size is to make sure the density of the shipis such that it will float on water. Density is defined as the ratio of mass tovolume.
  • Why the Titanic SankThe density of water is defined as 1. So in order for the Titanic to float, itneeded a density less than 1.
  • Why the Titanic SankTo simplify the calculation of density, let’s assume that the bulk of the shipis in the shape of a triangular prism, as shown here.
  • Why the Titanic SankThe net on the left shows the three dimensions used to calculate thevolume of a triangular prism.
  • Why the Titanic SankThe length, width, and height measurements are those of the Titanic. Themass of the ship was 46,000 tons.
  • Why the Titanic SankThe measurements provided yield a density of 0.41 for the Titanic, wellbelow the density needed to float. This also means that the Titanic couldstill take on water before sinking.
  • Why the Titanic SankOnce the Titanic started taking on water, its mass would increase while itsvolume decreased. This is shown in the expression above. Losing volumeand gaining mass is a deadly combination that will lead to a ship sinking.
  • Why the Titanic SankWe can graph the function representing the changing density to see whereit intersects the graph y = 1. This is the point where the ship has taken ontoo much water, making its density greater than 1.
  • Why the Titanic SankOnce the ship gained about 40% more mass in water, then the ship hadtoo much density to float. One of the features that was intended to preventtoo much water was the set of 16 water-tight sections of the ship.
  • Why the Titanic SankHowever, when the Titanic struck the ice berg, five (possibly six)compartments were damaged. This would have allowed enough water tosink the Titanic.
  • Or would it?Click on this video to see what additional problems emerged with these water-tight compartments.http://youtu.be/xZ8Olj0xs4Q
  • Why the Titanic SankDo you think if the 16 compartments had been fully water tight that theTitanic might have stayed afloat long enough for the passengers to berescued?
  • This presentation was adapted from our Geometry Applications video series, “Area and Volume.” Click here for more information.http://www.media4math.com/Geomet