Posted 21 Sep 2012 (Okay yes, this was inspired by an xkcd comic...) Find the most accurate approximation (for the the units given) that has 5 characters or less (not counting negative sign or decimal point) for the following: 1) Gravitational constant: 6.673x10^-11 (m^3/kg/s) 2) Avogadro's number: 6.022x10^23 3) Planck's constant: 6.026x10^-34 (m^2*kg/s) 4) Electron mass: 9.109x10^-31 (kg) 5) Boltzmann constant: 8.617x10^-5 (eV/K) 6) Permittivity of free space: 8.854x10^-12 (F/m) 7) Elementary charge: 1.602x10^-19 C I.e. you could approximate a light-year as 99^8 (m). 0 Share this post Link to post Share on other sites

0 Posted 22 Sep 2012 (edited) here's all my answers 7^-12 5^34 56^-19 38^-19 22^-3 24^-8 22^-14 and here's my pseudo-code that produced it. for i in range(2,100): result = i**int(math.log(value,i)) if result/value > 1: result = result/value-1 else: result = 1-result/value if result < aprox: aprox = result index = i exponent = int(math.log(value,i)) print(index,exponent) Edited 22 Sep 2012 by phil1882 0 Share this post Link to post Share on other sites

0 Posted 23 Sep 2012 That's pretty good. In case my example confused anyone, you can also use things besides exponents (including operators), and you can use non-integers in exponents. Heck, go ahead and throw in pi (it can count as one character) and e if you want for fun . 0 Share this post Link to post Share on other sites

0 Posted 24 Sep 2012 May be cheating but Avogadro's constant=R/K 0 Share this post Link to post Share on other sites

0 Posted 24 Sep 2012 Pi^{47.83 }Still trying to make it better/nicer. 0 Share this post Link to post Share on other sites

0 Posted 26 Sep 2012 I came up with some others. 1) Pi^{-7.53e} 5) 19.67^{-Pi} 6) e^{-25.45} 7) Pi^{-37.8} I went the Pi/e route.Planck's constant and Electron mass are still giving me troubles with using Pi or e. 0 Share this post Link to post Share on other sites

Posted

(Okay yes, this was inspired by an xkcd comic...)

Find the most accurate approximation (for the the units given) that has 5 characters or less (not counting negative sign or decimal point) for the following:

1) Gravitational constant: 6.673x10^-11 (m^3/kg/s)

2) Avogadro's number: 6.022x10^23

3) Planck's constant: 6.026x10^-34 (m^2*kg/s)

4) Electron mass: 9.109x10^-31 (kg)

5) Boltzmann constant: 8.617x10^-5 (eV/K)

6) Permittivity of free space: 8.854x10^-12 (F/m)

7) Elementary charge: 1.602x10^-19 C

I.e. you could approximate a light-year as 99^8 (m).

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