Unapproximable Numbers

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A mathematics talk given by Colin Wright, this starts with the well-known question about the value of pi, and explores where that goes.

It's well-known that 22/7 is a reasonable approximation to pi. Indeed, some people even mistakenly believe that pi is equal to 22/7, not realising that the ratio of a circle's diameter to its circumference can never be given exactly by a fraction.

Less well-known, however, is the approximation 355/113, a value that's accurate to better than 1 part in 10 million.

How can such approximations be found? Why are they so good? Does every number have a good approximation, and if not, which numbers cannot be approximated?

Connections are made to computer graphics, computer security, plant growth, breeding rabbits, and aesthetics.

If you're interested in knowing more, let us know.


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