Math Topics/Physics - Connections to the PCMI Theme Summary
Tuesday, July 1, 2003
On Tuesday, July 1, we started by further exploring the difference tables which we worked on in the morning with Bowen and Ben. Later Beverly led us in a simple experiment using CBR equipment to measure temperature.
First, we extended the idea of finding patterns in difference tables to functions of the form f(x)= k^x where k is an integer. We proved that anywhere in the difference table to get to the next box to the right, multiply by (k-1). To go down a box, multiply by k. To go right n boxes, multiply by (k-1)^n. Another function we looked at was f(x)= Fibonnaci numbers, i.e., f(1)=1, f(2)=1, f(3)=2, f(4)=3, and so on. The difference table was remarkable in its symmetry over a diagonal line of zeros and also because by reading it from right to left the Fibonnaci algorithm was present, only this time, with alternating negative and positive numbers.
The experiment with the temperature probes and cups of hot water was very helpful to those of us unfamiliar with the TI equipment. Lisa informed us that if we did not have the calculators and would like to introduce them to our schools, we could call 1-800-TI-CARES to ask them to loan them to us for a couple of days.
We all made graphs of the temperature of the hot water in our respective coffee cups and occasionally took out and reinserted the probe to see the effects on the graphs.
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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.