Math in the News: 8/29/11

8/29/11

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.

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.

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.

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.

Hurricanes

• But this random walk needs to be a bit less random if we want the path to generally go along a northwest path.

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.

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?

Hurricanes• Add two column

headings, x and y, to A1 and B1.

• Input the coordinates (10, -10) in A2 and B2.

Hurricanes• Add this formula to

cell A3.

• Then input this formula into cell B3

Hurricanes• Copy and paste the

formulas in cells A3 and B3 to enough cells to create 20 ordered pairs.

Hurricanes

• Graph the data.

Hurricanes

• Overlay a map of the region to see the simulated path of the hurricane.

Hurricanes

• Run different simulations to model different paths.

Hurricanes

• Tweak the randomization formulas to affect the amount of northern and western tracking.

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.