• Write a program to explain in several pages how Eratosthenes' sieve works to produce all prime numbers between 0 and 100.
  • In the Poincaré model of non-Euclidean geometry, the geodesic lines are the arcs interior to the unit circle perpendicular to its boundary. Define a method with points P, Q as arguments that draws the `line' between them.
  • Graph the Bessel function

    J0(x) = 1 - (x/2)2 + (x/2)4/2!2! - (x/2)6/3!3! + ...

    for 0 ≤ x < 50.