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Carousel math

I'm sure this is a really dingy question, but I can't seem to get my brain
around the math this morning.

When planning a carousel book (three or more concertinas of sequentially
larger widths sewn together at the fore edge to create little "scenes" when
the book is opened cover to cover like a star), is there a simple equation
when figuring out the width of the first and last pages so that the depth of
the last pages (radius) and the width of the front pages (which will form
the circumference) allow the book to open with the best view of all the
scenes? I want the front pages as open as possible, with enough depth to the

Thanks in advance -
(the mathmatically challenged)

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