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Extracting Pi from Image Data

image

Mandrill

samples

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recalculate

π approximation

3.12322

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:Symbol fr appears in multiple contexts {Notebook$$17$435917`,Notebook$$10$435904`}; definitions in context Notebook$$17$435917` may shadow or be shadowed by other definitions.

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:Symbol pi appears in multiple contexts {Notebook$$17$435917`,Notebook$$10$435904`}; definitions in context Notebook$$17$435917` may shadow or be shadowed by other definitions.

In 1881, Ernesto Cesàro [1] proved that the probability that two random integers are relatively prime is

≈0.61

. In this Demonstration, the pairs of random integers are chosen from among the pixel values of selected images.

Using enough random pairs of pixel data from almost any sufficiently complex picture gives an approximation of

with between 1 and 4 correct digits.

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