Today we had a real treat. We hosted speaker Glen Whitney at our school. Glen Whitney is the executive director of the Math Museum which will open in the Spring of 2012 in Manhattan, if all goes well. Twenty-three of our students joined Glen for a tour around the neighborhood, looking for math (Calculus, specifically) in the world around us. Thank you, Glen! And thank you to the USA Science & Engineering Festival and its sponsors for making it all possible.
We made four stops on our trip today:
- We stopped in the parking lot to look for Calculus. Some astute students noticed our Rocket with tangential trajectory to its curved support; the cars all around us that brought to mind position, velocity, and acceleration; the weather patterns (a continuous differentiable function on the globe!); the rate of student arrival/departure at school–an important consideration for those planning parking/drop-off patterns; and the chemical changes that cause leaves to fall off of trees.
- Then we moved up to the sidewalk by the baseball field. We did two different experiments simultaneously. Some students rolled PVC pipe down inclined sidewalks, and some bounced balls and measured the height of the bounce against time. In both cases we saw the affects of constant acceleration on the velocity and the position of the objects under consideration.
- Our third stop was at a set of telephone polls with a high-tension wire stretched between them. The wire formed a curve as it hung down and we wondered what that curve might be. Glen, with help from our students, derived the equation for the catenary/hyperbolic cosine (a favorite topic of mine!). The derivation involves a differential equation, the arc length formula, and some mathematical modeling–free body diagrams and all!
- Lastly, we stopped outside a church with a steeple and wondered about the mass of the steeple. We couldn’t climb up, take it down and weigh it. So we had to figure out some ways to make assumptions and gather data from the ground. We assumed it was a hollow cone, 10 cm thick. We used some Calculus to get a formula for the surface area. And we used some trig and inclinometers that we made to figure out the height. From that, we plugged into our equations and estimated the mass of the steeple to be approximately 8 metric tons.
When we came back some of us had lunch with Glen and spoke with him some more. For those that missed him, go visit him on the mall this weekend in DC. Everyone needs to go to the USA Science & Engineering Festival. I’ll be there, so you can come hang out with me :-).
Eventually I’ll post a few photos from our little field trip. So stay tuned.
Many thanks Glen, for all the good times!