Just for curiosity, how good an approximation can you find for π using an nth-root of an integer (a^1/n), or ( a^m/n).
State your accuracy (no. of decimal places).
It's surprising that you can find small numbers that do a pretty good job:
10^1/2 = 3.16 (1dp accurate)
31^1/3 = 3.1414 (3dps)
97^1/4 = 3.14 (2dps)
306^1/5 = 3.1416 (4 dps)
3020^1/7 = 3.141549 (3 dps)
29809^1/9 = 3.141591 (5 dps)
...
To find such approximations, simply raise π^n for some n, round up/down to nearest integer, then take the nth root.
(This doesn't really have much application, unless you can suggest one where π appears exponentiated, or you really need an approximation to (say) compute the volume of a hyphersphere :) )
2007-07-22
03:37:52
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3 answers
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asked by
smci
7