Posted 21 Sep 2012 · Report post (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) · Report post 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 · Report post 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 · Report post 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 · Report post 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 · Report post 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

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(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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