Hidden Harmonies by Ellen Kaplan

Author:Ellen Kaplan
Language: eng
Format: epub
Publisher: Bloomsbury Publishing
Published: 2013-09-15T04:00:00+00:00

The wonders of calculus allow us to determine the areas of such lacework (the integral began its life with just this aim), by extending the notion of triangulating you saw in Chapter Four—dividing and conquering to the limit.q At the same time, it extends the notion of what can have area—but only so far. Too many holes, too close together, and area evaporates. That would be true, for instance, of the famous Sierpin-ski Gasket, made by deleting the ‘midpoints triangle’ from an original triangle, then the midpoints triangles from those remaining—and so on, forever. The area of what’s left turns out to be zero (a quarter of what was

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