Trident gum is related to mythology because it shares a name with the weapon of choice of the Greek god Poseidon. Poseidon, the god of the sea in Greek mythology, carries a trident, a type of three-pronged spear commonly used in fishing. He uses the trident to create storms.
The word "trident" comes from a Latin phrase that means "three teeth." Poseidon's trident had three prongs that resembled teeth. The makers of Trident gum chose the name because the gum originally contained three enzymes to reduce the risk of tooth decay. The shared name is the only connection between Poseidon's trident and Trident gum.