You could use the attributes of a Triangle object directly (of which there
are many, including area):
>>> p=Point
>>> A = p(0, 0)
>>> B = p(3, 0)
>>> C = p(3, 3)
>>> Triangle(A,B,C).area
9/2
or simplify your "manual" result:
>>> simplify(sqrt(-3*sqrt(2)/2 + 3)*sqrt(27*sqrt(2)/4 + S(27)/2))
9/2
/c
On Sunday, May 17, 2015 at 3:07:48 PM UTC-5, ravas wrote:
>
> My goal is to input the coordinates of the vertices of a triangle and have
> significant properties printed for a human to read.
> I'm aware of the limitation of floating point arithmetic, and I was able
> to produce an accurate area with the decimal module.
>
> return (sp*(sp-a)*(sp-b)*(sp-c)).sqrt().quantize(dec('1.0000000000'))
>
> However, a version using sympy is also desirable. Do I need to install
> mpmath / gmpy to compensate for the floating point errors?
> Here is the test code:
>
> import sympy.functions as sym
> import sympy.geometry as geo
>
> sqrt = sym.sqrt
>
> def distance(A, B):
> """
> A & B are objects with x and y attributes
> :return: the distance between A and B
> """
> dx = B.x - A.x
> dy = B.y - A.y
> return sqrt(dx**2 + dy**2)
>
> def sides(A, B, C):
> """
> A, B & C are objects with x and y attributes
> :return: sorted side lengths (smallest to largest)
> """
> a = distance(B, C)
> b = distance(A, C)
> c = distance(A, B)
> return sorted((a, b, c,), key=float)
>
> def area(a, b, c):
> """
> a, b & c are the side lengths of the trigon
> :return: area of the trigon
> """
> p = a + b + c # perimeter
> sp = p / 2 # semi-perimeter
> return sqrt(sp*(sp-a)*(sp-b)*(sp-c))
>
> if __name__ == '__main__':
> p = geo.Point
> A = p(0, 0)
> B = p(3, 0)
> C = p(3, 3)
> sides = sides(A,B,C)
> print(sides)
> print(area(*sides))
>
> Output:
>
> [3, 3, 3*sqrt(2)]
> sqrt(-3*sqrt(2)/2 + 3)*sqrt(27*sqrt(2)/4 + 27/2)
>
> Obviously I want 9/2 as the result for the area... but it is giving me a
> representation of 4.4999999999...
> What can I do about this?
>
>
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