John Botzum, Kutztown University of Pennsylvania
Villanova University (Villanova, PA)
The Philadelphia Area Seminar on History of Mathematics will meet on Thursday, April 19, 2018, from 6:00 p.m. to 8:00 p.m. in Saint Augustine Center, Room 300.
We begin with conversation and a light supper (donation $10.00). About 6:30-6:45 the talk will begin, when Professor John Botzum of Kutztown University of Pennsylvania will speak on:
The Phi-bonacci Sequence
Sometimes innocent questions from students can stir long-forgotten memories and stimulate mathematical investigation. Last year I took over my wife’s Discrete Mathematics course for a week. I spent much of the first class working out elementary induction proofs and introducing recurrence relations. At the end of the class one of the students asked if there were a recurrence relation for the nth term of the Fibonacci sequence. I was in a hurry to teach a class 45 minutes away so I foolishly replied that I did not think there was. On the drive to my other job I recalled Binet’s formula which prompted me to dig up notes on this subject that I had long since forgotten. This paper will discuss my discovery and re-discovery of the beautiful interplay between Binet’s recurrence relation, the Golden Mean,and the Fibonnaci Sequence as well as discuss whether Binet was the first to discover the formula.
Directions:
Villanova University is located on Route 30, Lancaster Avenue, just east of I-476. If you drive to the meeting, enter Villanova by the main gate on Ithan Avenue. By order of the Parking Office all parking is now in the Saint Augustine Center lot, newly refurbished to a multistory structure. You will need to display a parking pass, which will follow in a later email. The Saint Augustine Center is attached to the lot, and Room 300 is on the third floor. You can get in touch with me (Alan Gluchoff) at 610-905-1376 if you need help.
Public Transportation: Take SEPTA’s Paoli-Thorndale train to the Villanova station. If outbound from center city go down through the tunnel to the inbound side. From the inbound platform go up the stairs and proceed to the left. The second building you encounter is the SAC; entry is through the parking lot or the front entrance.