Place the hardwood board flat on a work surface. Form the flexible ruler on one 18-inch edge of the board to create a graceful curve for the back of the rocking chair seat. Trace along the ruler to transfer the curve to the board using a pencil.
Form the ruler along the opposite edge of the board to create rounded curves on the front corners of the seat. Trace along the ruler to transfer the curves to the board with a pencil.
Saw along the pencil lines on the board using a band saw. Guide the board through the saw in a steady motion, just fast enough to allow the blade to cut through the wood until the curves are cut out.
Cut around the top and bottom edges of the board using a router equipped with a 1/4-inch round-over bit. This will provide a rounded edge along both the top and bottom sides of the rocking chair seat.
Sand the routed edges of the seat with a fine-grit sanding pad in the same direction as the wood grain until the wood is completely smooth.