The Dresden ruler is great to work with and not very expensive.

QuiltnNan has the right pattern, which looks like what you have described. You can make this block, piecing it completely, however, I might consider doing machine applique or even hand applique for the fan. Having made this pattern before many years ago, getting the curves to get together can be a little tricky, but of course it's your quilt.

Of all the places to see one like you are describing, The Beverly Hillbillies has a fan quilt on their truck in a lot of episodes
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Sorry it has taken so long to get this picture up - I wanted to wait until the quilt was pretty much finished before taking it. It must be a Grandmother's Fan variant, but I am curious whether it has its own name...