Heronian triangles: Difference between revisions
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→{{header|Python}}: (Replaced deprecated fractions.gcd with math.gcd)
m (→{{header|Python}}: (Replaced deprecated fractions.gcd with math.gcd)) |
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Line 3,634:
<lang python>from __future__ import division, print_function
from math import gcd, sqrt
from itertools import product
Line 3,641 ⟶ 3,640:
def hero(a, b, c):
s = (a + b + c) / 2
a2 = s * (s - a) * (s - b) * (s - c)
return sqrt(a2) if a2 > 0 else 0
def is_heronian(a, b, c):
a = hero(a, b, c)
return a > 0 and a.is_integer()
def gcd3(x, y, z):
return gcd(gcd(x, y), z)
Line 3,656 ⟶ 3,655:
if __name__ == '__main__':
maxside = 200
h = [(a, b, c) for a, b, c in product(range(1, maxside + 1), repeat=3)
if a <= b <= c and a + b > c and gcd3(a, b, c) == 1 and is_heronian(a, b, c)]
h.sort(key = lambda x: (hero(*x), sum(x), x[::-1])) # By increasing area, perimeter, then sides
print('Primitive Heronian triangles with sides up to %i:' % maxside, len(h))
print('\nFirst ten when ordered by increasing area, then perimeter,then maximum sides:')
print('\n'.join(' %14r perim: %3i area: %i'
% (sides, sum(sides), hero(*sides)) for sides in h[:10]))
print('\nAll with area 210 subject to the previous ordering:')
print('\n'.join(' %14r perim: %3i area: %i'
% (sides, sum(sides), hero(*sides)) for sides in h
if hero(*sides) == 210))</lang>
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