The ring which makes the small configuration truly circular is clearly not of uniform width. I can see this and know that it's absolutely necessary. This table idea would generalize to area ratios > 2 with considerable added complexity, including having more than two layers when in the small configuration. (I'm not contending that this would be practical.) The way they achieve very small gaps is simply to size and shape all pieces extremely accurately. Modern large production woodworking machinery makes this a bit easier but great craftsmanship is still needed, especially since wood expands and contracts nonisotropically with varying moisture in the air. I've done a fair amount of woodworking but I'd never attempt this. Steve Gray Ed Pegg Jr wrote:
A nifty circular table based on dissections is available. With a spin, it becomes a table twice as large as before. The mechanism is beautiful.
Fletcher Capstan Tables http://www.dbfletcher.com/capstan/
--Ed Pegg Jr
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