Hello all,
Consider the program below which is an attempt to prove that the angle
inscribed at the center by any two points on a circle is always twice
the angle inscribed on the circumference:
from sympy import Circle, Point, Segment
def prove_theorem():
c = Point(0, 0)
c1 = Circle(c, 2)
p = c1.random_point()
q = c1.random_point()
r = c1.random_point()
pc = Segment(p, c)
qc = Segment(q, c)
pcq = pc.angle_between(qc)
pr = Segment(p, r)
qr = Segment(q, r)
prq = pr.angle_between(qr)
print((pcq/prq).evalf())
if __name__=='__main__':
for _ in range(100):
prove_theorem()
The result which should always be 2.00 theoretically ranges from
0.533910696827908 to 26.3044198350215.
The only source of this randomness seems to be the random_point()
method. But, is such a huge variance expected? Is there a way to
minimize this variance?
Thanks for any hints.
Best,
Amit.
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