I do love geometry and trigonometry! This one really got my brain working and
it was really fun to do. I drew many many pictures and spent time relearning
all I used to know of trig. Despite this, I kept getting the wrong answer. I
checked my work about 5 times and everytime saw that I was doing it correctly.
I finally realized that it was the value for l_section_area that I’d
miscalculated. Here’s all this hard trig and I’m fine, but some simple
sibtraction I couldn’t even do! Upon fixing that I was able to get the answer
super fast!
import math
l_section_area = 1 - (math.pi / 4)
def solve(n):
k = 1
while percent(k) > n:
k += 1
return k
def percent(n):
theta = math.atan(1 / n)
alpha = math.asin((n - 1) / (n ** 2 + 1) ** 0.5)
beta = math.pi / 2 - theta - alpha
segment_area = (beta - math.sin(beta)) / 2
triangle_area = (1 - math.cos(beta)) / 2
concave_triangle_area = triangle_area - segment_area
return concave_triangle_area / l_section_area
if __name__ == '__main__':
import sys
n = eval(sys.argv[1])
print(solve(n))
import pytest
from problem import solve, percent
_test_percent = (
(1, 0.50),
(2, 0.36462616929172803),
)
@pytest.mark.parametrize('n,expect', _test_percent)
def test_percent(n, expect):
assert expect == percent(n)
_test_solve = (
(0.10, 15),
)
@pytest.mark.parametrize('n,expect', _test_solve)
def test_solve(n, expect):
assert expect == solve(n)