### July 6-11, 1998 - Swarthmore, Pennsylvania

1998 Summer Institute || Participant Projects || List of Participants || Sum98 Staff || Agenda

## If Only Nice Weather Could Last Year Round

### Math Forum Advanced Web Institute, Shared Lesson

#### Evan Glazer

Objective: To make connections between monthly temperature data and sinusoidal modeling.

1. Access temperature data from http://nimbo.wrh.noaa.gov/Reno/max.htm

2. Use the temperature data from Savannah, Georgia, to derive a model in the form:

Y = Acos(B(x - c)) + D

Let X = month # and let y = temperature.
For example, when x = 6.5, the corresponding data is June 15.

Note: The first column and last column in the data set should not be used. The 30 in the first column represents the number of years the data was collected, and the last column represents the average temperature in one year.

 Month Month# Temperature Jan 1 Feb 2 Mar 3 Apr 4 May 5 Jun 6 Jul 7 Aug 8 Sep 9 Oct 10 Nov 11 Dec 12

3. Interpret the physical properties associated with A, B, C, and D in the equation.

4. If you only enjoyed temperatures between 6t and 85 degrees, during what time intervals (dates) would you live in Savannah, Georgia?

5. Look at the student project for this activity at:
http://www.glenbrook.k12.il.us/gbsmat/temp/temp.html

6. Note that sinusoidal temperature patterns also occur hourly at:
http://www.ems.psu.edu/cgi-bin/wx/tempstats.cgi

7. Watch periodic motion when you play music at:
http://www.frontiernet.net/~imaging/play_a_piano.html

8. A mathematical perspective on the weather can be found at:
http://www.naples.net/weather/humor.htm