Types of fins and fish swimming
The fins of bony fish are appendages made of protruding bone spines joined together by thin skin.
The caudal fin (“tail”) helps the propulsion of the fish. The anal and dorsal fins have a function of stability, when moving slowly or when stopped. The pectoral and pelvic (ventral) fins allow the fish to adjust its trajectory (direction changes up + down + right + left), to accelerate or slow down; they also have a role in stabilizing.
Common goldfish have one single dorsal, caudal and anal fin, while the pelvic and pectoral fins are paired. But depending on the variety, these characteristics can be very different: for example, in a more sophisticated variety, such as the Ryukin, all the fins are paired except the dorsal fin.