A 3, 4, 5 triangle is a triangle with edge lengths 3, 4, and 5. It is the right triangle with
smallest possible integer lengths and corresponds to
the Pythagorean triple 
where the legs have lengths
3 and 4 and the hypotenuse length 5. It satisfies
the Pythagorean theorem since
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(1)
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It has inradius
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(2)
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Triangle line picking for two points chosen independently from a uniform distribution in a 3, 4, 5 triangle gives a mean line segment length of
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(3)
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(4)
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(E. W. Weisstein, pers. comm., Aug. 6-9, 2010; OEIS A180307).
