### Mathematics Research Projects

## Project 11: Visibility of Equilateral
Polygons

**Problem**

1. Is the visibility theory of equilateral plane polygons (i.e.
ones in which all sides of the polygon have the same length) identical
to the theory of general plane polygons? In other words are there
theorems that are true for plane equilateral polygons which do
not hold for general polygons?

**Extensions**

1. Extend your work to the situation where one has polygons with
"holes," that is, consider the case of having equilateral
polygons with equilateral holes.

**References**

1. O'Rourke, J., Art Gallery Theorems and Algorithms, Oxford University
Press, New York, 1987.

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**Joseph Malkevitch**

*Department of Mathematics and Computing*

York College (CUNY)

Jamaica, New York 11451-0001

email: malkevitch@york.cuny.edu

(Comments and results related to the project above are welcome.)

**Acknowledgements**

Some of this work was prepared with partial support from the National
Science Foundation (Grant Number: DUE 9555401) to the Long Island
Consortium for Interconnected Learning (administered by SUNY at
Stony Brook, Alan Tucker, Project Director).