Download - Math in the News: 8/29/11
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8/29/11
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Hurricanes
• The specific path that a hurricane takes can’t be accurately predicted because of the many variables involved.
• But the general path that a hurricane takes is in a northwestern direction.
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Hurricanes
• One way to model the behavior of a hurricane is to use a “random walk” simulation.
• Imagine an ant on a coordinate grid and the random walk it would take across it.
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Hurricanes
• You can create a random walk using an Excel spreadsheet.
• The data in the table, represented in the graph, was generated using a random number formula.
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Hurricanes• Add two column
headings, x and y, to A1 and B1.
• Start at the origin. Enter 0 in A2 and B2.
• Enter this formula (shown for A3) in subsequent rows:
=A2+RANDBETWEEN(-2,2)
• Do the same for Column B.
• Graph the data.
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Hurricanes
• But this random walk needs to be a bit less random if we want the path to generally go along a northwest path.
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Hurricanes
• If we place an x-y coordinate grid as shown on a map, then the random path should start in quadrant 4 and move along a negatively sloped path.
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Hurricanes
• In other words, the randomization should favor a step to left than one to the right, and a step upward than one downward.
• How can we influence the randomization this way?
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Hurricanes• Add two column
headings, x and y, to A1 and B1.
• Input the coordinates (10, -10) in A2 and B2.
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Hurricanes• Add this formula to
cell A3.
• Then input this formula into cell B3
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Hurricanes• Copy and paste the
formulas in cells A3 and B3 to enough cells to create 20 ordered pairs.
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Hurricanes
• Graph the data.
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Hurricanes
• Overlay a map of the region to see the simulated path of the hurricane.
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Hurricanes
• Run different simulations to model different paths.
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Hurricanes
• Tweak the randomization formulas to affect the amount of northern and western tracking.
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Hurricanes
• Scientists use sophisticated computer models to predict the path of a hurricane.
• But because of the many variables involved, predicting a hurricane’s path with a high degree of accuracy is difficult.