Infinite froth

Foam Products. Latices are made into foams for use in cushioning appHcations. The latices are frothed with air and then chemically coagulated for thick appHcations, or heated to induce coagulation for thinner appHcations. The latter method allows for infinite pot life during production (see Foamed plastics). 

Such thoughts of an infinite froth need not be confined to mere armchair speculation. In fact, we can construct and explore such a froth that inhabits the realm of abstract geometry. Moreover, the froth we will make is not simply an artistic design created from some arbitrary mathematical recipe, but rather it comes about naturally from the study of the little-known Ford circles, named after L. R. Ford, who published on this topic in 1938. Ford circles provide an infinite treasure chest to explore, and the circles are among the most mind-numbing mathematical constructs to contemplate. In fact, it turns out that they describe the very fabric of our rational number system in an elegant way. ... 

In Fractal Milkshakes and Infinite Archery you ll learn about a bubbly froth lurking in the fabric of our number system. The foam is comprised of an infinite regression of circles known as Ford circles. (A graphical representation of the froth is placed on page ix to whet your appetite.)... 

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