45 lines
1.2 KiB
Python
45 lines
1.2 KiB
Python
from __future__ import division, print_function
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from math import gcd, sqrt
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def hero(a, b, c):
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s = (a + b + c) / 2
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a2 = s * (s - a) * (s - b) * (s - c)
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return sqrt(a2) if a2 > 0 else 0
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def is_heronian(a, b, c):
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a = hero(a, b, c)
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return a > 0 and a.is_integer()
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def gcd3(x, y, z):
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return gcd(gcd(x, y), z)
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if __name__ == '__main__':
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MAXSIDE = 200
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N = 1 + MAXSIDE
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h = [(x, y, z)
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for x in range(1, N)
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for y in range(x, N)
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for z in range(y, N) if (x + y > z) and
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1 == gcd3(x, y, z) and
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is_heronian(x, y, z)]
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# By increasing area, perimeter, then sides
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h.sort(key=lambda x: (hero(*x), sum(x), x[::-1]))
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print(
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'Primitive Heronian triangles with sides up to %i:' % MAXSIDE, len(h)
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)
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print('\nFirst ten when ordered by increasing area, then perimeter,',
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'then maximum sides:')
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print('\n'.join(' %14r perim: %3i area: %i'
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% (sides, sum(sides), hero(*sides)) for sides in h[:10]))
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print('\nAll with area 210 subject to the previous ordering:')
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print('\n'.join(' %14r perim: %3i area: %i'
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% (sides, sum(sides), hero(*sides)) for sides in h
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if hero(*sides) == 210))
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