Math in the News: 8/29/11


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In this issue of Math in the News we look at how to develop computer models for tracking the path of a hurricane.

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Math in the News: 8/29/11

  1. 1. 8/29/11
  2. 2. Hurricanes <ul><li>The specific path that a hurricane takes can’t be accurately predicted because of the many variables involved. </li></ul><ul><li>But the general path that a hurricane takes is in a northwestern direction. </li></ul>
  3. 3. Hurricanes <ul><li>One way to model the behavior of a hurricane is to use a “random walk” simulation. </li></ul><ul><li>Imagine an ant on a coordinate grid and the random walk it would take across it. </li></ul>
  4. 4. Hurricanes <ul><li>You can create a random walk using an Excel spreadsheet. </li></ul><ul><li>The data in the table, represented in the graph, was generated using a random number formula. </li></ul>
  5. 5. Hurricanes <ul><li>Add two column headings, x and y, to A1 and B1. </li></ul><ul><li>Start at the origin. Enter 0 in A2 and B2. </li></ul><ul><li>Enter this formula (shown for A3) in subsequent rows: </li></ul><ul><li>=A2+RANDBETWEEN(-2,2) </li></ul><ul><li>Do the same for Column B. </li></ul><ul><li>Graph the data. </li></ul>
  6. 6. Hurricanes <ul><li>But this random walk needs to be a bit less random if we want the path to generally go along a northwest path. </li></ul>
  7. 7. Hurricanes <ul><li>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. </li></ul>
  8. 8. Hurricanes <ul><li>In other words, the randomization should favor a step to left than one to the right, and a step upward than one downward. </li></ul><ul><li>How can we influence the randomization this way? </li></ul>
  9. 9. Hurricanes <ul><li>Add two column headings, x and y, to A1 and B1. </li></ul><ul><li>Input the coordinates (10, -10) in A2 and B2. </li></ul>
  10. 10. Hurricanes <ul><li>Add this formula to cell A3. </li></ul><ul><li>Then input this formula into cell B3 </li></ul>
  11. 11. Hurricanes <ul><li>Copy and paste the formulas in cells A3 and B3 to enough cells to create 20 ordered pairs. </li></ul>
  12. 12. Hurricanes <ul><li>Graph the data. </li></ul>
  13. 13. Hurricanes <ul><li>Overlay a map of the region to see the simulated path of the hurricane. </li></ul>
  14. 14. Hurricanes <ul><li>Run different simulations to model different paths. </li></ul>
  15. 15. Hurricanes <ul><li>Tweak the randomization formulas to affect the amount of northern and western tracking. </li></ul>
  16. 16. Hurricanes <ul><li>Scientists use sophisticated computer models to predict the path of a hurricane. </li></ul><ul><li>But because of the many variables involved, predicting a hurricane’s path with a high degree of accuracy is difficult. </li></ul>