I've also done quite a bit of experimenting with making the geese fly in a circle and paper piecing is my savior. I made three gifts with a similar theme for three friends who had birthdays in January and February.
Jim was gifted with a two bottle wine carrier and a pouch that holds a reusable ice pack in case the wine is white - or in case room temp is just too hot as is often the case of a Southern summer.
Alice, an inveterate knitter who seldom ventures out without a project, received a project bag along with an accessory pouch to hold all the etcetera that usually floats around in the bottom of a craft bag.
Here is another view that shows detachable shoulder strap.
And Joan received this table topper/hot pat/wall hanging. Yeah, I know, but it really could work as any of those. It has pockets for hanging, is insulated, and could be just decorative on the table.
Each of the circles is made up of four paper pieced sections, and though it looks a bit complex, it really is easy peasy. Paint by numbers for quilters!
Here you can see how the sections were assembled for each piece.
This is the template I drew up. I made my template at 6 1/2 inches so that the finished circle would be 12 1/2 inches, but you really could make it any size. Feel free to reproduce it either by copying the picture and inserting it into another document or application, or by using this as a guideline to draft your own.
And if you aren't an expert paper piecer, by all means take Amy Gibson's free class on Craftsy.com. In the 2012 Block of the Month class she gives and excellent explanation of how to paper piece.
The only thing I would add to her instructions relates to perforating the paper. Amy recommends that you use your sewing machine without thread to quickly perforate the paper along the seam (and future tear) lines. While this works really well, it is hard on the sharpness of your needle.
I recently learned a new trick and now I use my tracing tool to quickly perforate the seams. I like this one from Dritz. Give it a try and let me know what you think.