I want to write a function
golf(C, A) that takes the height (
C = 2*c) and the width (
A = 2*a) of an oblate (left image) or prolate (right image) spheroid or a sphere as parameters and returns the volume
V and the surface area
S of the shape as tuple. The output must be rounded to two decimal places.
All input and output numbers are floating point decimals.
The input numbers (
C) are guaranteed to be greater than 0 and lower than 100.
Here are some example calls of the function (
golf(C, A)) in Python 3 and the expected outputs given as test cases:
golf(4, 2) # expected output (8.38, 21.48) golf(2, 2) # expected output (4.19, 12.57) golf(2, 4) # expected output (16.76, 34.69)
The challenge requires my code to be smaller than 150 characters.
I could not manage to solve it myself yet, my best solution in Python 3 still takes 220 characters:
from math import * def golf(C,A): c,a,V=C/2,A/2,pi/6*A*A*C;F=c*c/a**2;E=sqrt(1-(F if a>c else 1/F));S=4*pi*a*a if a==c else 2*pi*a*a*(1+(((1-E**2)/E)*atanh(E)if a>c else(c/(a*E))*asin(E))) return round(V,2),round(S,2)
The necessary formulas are taken from Wikipedia: Spheroid, here's a summary:
Vall spheroids = 4 π/3 a²c = π/6 A²C as A=2a and C=2c.