Given a circle, two chords are drawn at random. The task is to find the probability that these chords will intersect.
Consider two chords represented as vectors p = (p1, p2)
and q = (q1, q2)
in the unit circle. The parametrization functions of the chords are denoted as lambda_p(s) = (1-s)p1 + sp2
and lambda_q(t)
. Chords intersect if there exist s0
and t0
such that lambda_p(s0) = lambda_q(t0)
. This is expressed as a matrix equation Ax = b
, where x = (s, t)
and A
is formed by vectors (p1-p2)
and (q1-q2)
.
The provided code, written in SAS IML, simulates the probability of intersecting chords on the unit circle through random chord generation.
-
IntersectSegsSimple Function: Finds the intersection between two 2D line segments. Assumes different slopes (nonsingular matrix).
-
Simulation (Main Part): Generates random chords on the unit circle, simulates the probability of intersection, and prints the result.
- Ensure you have SAS IML installed.
- Run the code to simulate and estimate the probability.
- Modify the
N
variable to control the number of simulations.
Feel free to experiment with the code based on your requirements.