Here's something to think about for fun: Calculating an Expanding Square (Microsoft Excel) The link provides a download for a spreadsheet that will calculate the points for a search and rescue effort that starts at a center point and then expands from that location in a spiraling rectangle. (It says that it creates an expanding square, but that only sort of works near the equator; for other areas it is a rectangle.) Once you download the spreadsheet, you can "unprotect" the worksheet (there is no password) so that you can format the table array to bring the data into ArcMap. If you add a column for "Line" and calculate all of the rows to be "1", you can use the Data Management Tools-->Features-->Point to Line script to convert the points into a line using the "Seg" column as the sort order. The spreadsheet formulas have some obvious issues, but it is a quick approximation of what someone might need. If you were going to improve the solution in ArcGIS so that it was a more accurate expanding square, how would you do it?

The example uses an approximation of geographic coordinates. It's kind of cool how they set up the even/odd routine. You can (perhaps) do better letting ArcGIS handle the coordinates through a projection (spatial reference).

In Python: