Approximations

[Yoruichi-san]

(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).

[phil1882]

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 September 22, 2012 by phil1882

[Yoruichi-san]

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 .

[James33]

May be cheating but Avogadro's constant=R/K

[Rob_Gandy]

Pi^47.83 Still trying to make it better/nicer.

[Rob_Gandy]

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.