When young Per visits her uncle Sir Cumference, aunt Lady Di of Ameter, and her cousin Radius, they teach her how to play Inners and Edges. After Per finds a clue linking the game to the mysterious castle of the Countess Areana, she and Radius sail to the island of Immeter. There, they have to decipher cryptic clues while avoiding a sea serpent. To unlock the island's secret, Per has to figure out how to find the perimeter and area of a circle. Only then can she become Per of Immeter.