# Off on a Tangent 18.04

### Zeno’s paradox and more in next week’s colloquium

• Title: Zeno’s paradox, the harmonic series, and 1=1/2???
• Speaker: Dr. Stephanie Edwards
• When: Tuesday, October 29 @ 4:00 PM
• Where: VanderWerf 104

Abstract: Zeno’s paradox says that before one can get to position A, one must first get halfway there. Before one can get to the halfway point, one must get halfway to the halfway point, and so on.  Since this goes on forever, it seems that the distance cannot be covered. We will use geometric series to show that the distance will, indeed, be covered. We will also explore the harmonic series and show that rearrangements of the alternating harmonic series can lead to puzzling conclusions.

### Estimating areas talk coming up soon

• Title: Estimating areas
• Speaker: Dr. Paul Pearson
• When: Thursday, November 7 @ 4:00 PM
• Where: Schaap Science Center 1000

Abstract: Finding an accurate estimate for the area of an irregular shape can be hard to do.  One easy way to estimate the area is to lay a square grid over the shape and then count the squares that lie over the shape and multiply by the area of each square.  We will jazz up this method to a triangular grid and use an ingenious counting result discovered by Georg Pick to find the area of any polygonal shape with vertices on the grid.  To justify Pick’s result, we will use Euler’s formula V – E + F = 2 relating the vertices, edges, and faces of a connected planar graph.  These results are surprising because of their clever use of  basic tools from combinatorics and topology to solve the area estimation problem in geometry.  This talk is designed to be fun, interactive, and accessible to all students who have ever counted anything.  Students in math education are particularly encouraged to attend.  Please come and bring your friends (and a pencil!).

### Problem Solvers of the Fortnight

Congratulations to Meredith Bomers, Sarah Brown, Adair Cutler, Liz Cutlip, Adam Czeranko, Blake Engler, Fiona Johnson, Peter Le, David McHugh, Matthew Nguyen, McKenna Otto, Jack Radzville, Dan Romano, Bethany VanHouten, Tracy Westra, and Kamaron Wilcox — all of whom correctly solved the Problem of the Fortnight in the last issue of America’s premiere fortnightly mathematics department newsblog.

### Problem of the Fortnight

Determine F(x) if, for all real x and y,

F(x)F(y) – F(xy) = x + y.

Hint:  What could F(1) be?

Affix to your solution (not just the answer) to some oddments from your Halloween celebrations, and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson’s office, room 212 in The Werf, by 3:00 p.m. on Friday November 1.  As always, be sure to include your name and the name(s) of your math professor(s) — e.g. Hilda Brume, Professors Frank and Stein — on your solution.  Good luck and have fun!