** April 2000 **

Millersville University of Pennsylvania

Millersville PA

Contact:Ximena Catepillan Hearn, <ximena.hearn@millersville.edu>Short Description:Student Talks and The Sixth Annual Millersville University Honors and Awards Banquet

The Mathematics Department at Millersville University of Pennsylvania will be celebrating Mathematics Awareness Month for the year 2000 with the following activities. Student Talks. Thursday, April 27. Undergraduate students Anita Dale and Jim Fair will talk about the math modeling projects that they have completed under the direction of Dr. Robert Buchanan. The first project is a Math Modeling Contest problem from 1997. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ The Velociraptor Problem - by Anita Dale The velociraptor, Velociraptor mongoliensis, was a predatory dinosaur that lived during the late Cretaceous period, approximately 75 million years ago. Paleontologists think that is was a very tenacious hunter, and may have hunted in pairs or larger packs. Unfortunately, there is no way to observe its hunting behavior in the wild as can be done with modern mammalian predators. A group of paleontologists has approached your team and asked for help in modeling the hunting behavior of the velociraptor. They hope to compare your results with field data reported by biologists studying the behaviors of lions, tigers, and similar predatory animals. The average adult velociraptor was 3 meters long with a hip height of 0.5 meters and an approximate mass of 45 kg. It is estimated that the animal could run extremely fast, at speeds of 60 km/hr, for about 15 seconds. After the initial burst of speed, the animal needed to stop and recover from the buildup of lactic acid in its muscles. Suppose that velociraptor preyed on Thescelosaurus neglectus, a herbivorous biped approximately the same size as velociraptor. A biochemical analysis of a fossilized thescelosaurus indicates that is could run at a speed of 50 km/hr for long periods of time. Part I: Assuming the velociraptor is a solitary hunter, design a mathematical model that describes the hunting strategy for a single velociraptor stalking and chasing a single thescelosaurus as well as the evasive strategy of the prey. Assume that the thescelosaurus can always detect the velociraptor when it comes within 15 meters, but may detect the predator at even greater ranges (up to 50 meters) depending on the habitat and weather conditions. Additionally, due to its physical structure and strength, the velociraptor has a limited turning radius when running at full speed. This radius is estimated to be three times the animal's hip height. On the other hand, the thescelosaurus is extremely agile and has a turning radius of 0.5 meters. Part II: Assuming more realistically that the velociraptor hunted in pairs, design a new model that describes a hunting strategy for two velociraptors stalking and chasing a single thescelosaurus as well as the evasive strategy of the prey. Use the assumptions and limitations given in Part I. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Second project. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Modeling a Pinewood Derby Racer - by Jim Fair The Pinewood Derby is an annual event in which children race small wooden cars down a short inclined track. The cars are powered only by gravity. There is a small set of rules governing the size and weight of the cars. Examine the rules of the contest and devise an optimal design for a pinewood derby car. Answer such questions as: Does the weight distribution of the car affect its performance? What effect does rolling friction have on race times? What effect does air resistance have on race times? Also on Thursday, April 27, undergraduate students Michael Eber and Amy Newton will be presenting their projects relating abstract algebra to high school algebra. The Sixth Annual Honors and Awards Banquet. Friday, April 28 This is an opportunity for the Mathematics Department to honor its graduating seniors and those math majors receiving special awards.The key-note address for the banquet will be given by Distinguished Teaching Award Winner Dr. James Crawford from Lafayette College. His talk is entitled "How Much of Fermat's Last Theorem was Fermat Able to Prove".