Cabinet toy №3
Two Cubes, One Prime
Some primes are secretly two fractions cubed: 13 = (2/3)³ + (7/3)³. Pick a prime, start from one rational point on the curve x³ + y³ = p, and lay gold lines. A line through two rational points — or a tangent at one — meets the curve at exactly one more point, and that point is rational too. The fractions get very tall, very fast.
After rescaling, every curve here has the same shape. What changes is where the rational points land.
Choose a prime — shelves marked unreachable have no starting point small enough for our pockets.
Pick a point to start a seam.