Just an idea: you could plot the planet's trajectory in the rotating frame in which the suns are fixed:

Test plausibility of a proposition before investing effort in trying to prove it: det(AB) = ?

Sample without fear of seeing only special cases: contrast regular grid

Download and save this file but don't look at the contents: mystery.py. It defines a function f. Approximate the average of f by sampling it at linspace(0,1,17).

In digital computer, must be a deterministic scheme.

Mayfly model at b=4 generates "irregular", "chaotic", trajectories. Why no good for this purpose?

Random points on a dart board

How can the graph of a function densely cover a square?

What does the graph of y = 2x mod 1 over [0,1] look like? How about y = r0 + 2x mod 1? How about y = 3x mod 1?

LCG: Choose a multiplier a and a modulus m, both huge; and a starting integer (seed) i0.
Let *i*_{k + 1} = *a**i*_{k} mod *m*, and *r*_{k} = *i*_{k} ⁄ *m*.

# Linear congruential pseudo-random number generator rng_i = 17 # seed rng_a = 427419669081 # multiplier rng_m = 999999999989 # mod

infamous randu

# Linear congruential pseudo-random number generator "RANDU" # FAMOUSLY BAD. DO NOT USE! rng_i = 17 # seed rng_a = 2**16+3 # multiplier rng_m = 2**31 # mod

Exercise: Estimate the area of the flower whose boundary has the equation *r* = √(2 + cos7*θ*) in polar coordinates.

(Pick points at random in an enclosing rectangle and count the fraction of points that are inside the flower.)