According to Greek legend the half-sister of Alexander the Great, Thessalonike, turned into a mermaid when she tried ending her life by jumping into the sea. A white marble mermaid statue on the Greek island of Thasos commemorates this legend.
The legend involves Alexander finding the Fountain of Youth and making his sister immortal with its water. When Alexander later dies at the young age of 32, Thessalonike tries ending her own life by drowning. However, since she is immortal, she can’t die and is instead transformed into a mermaid. She has since inhabited the Aegean Sea, and when meeting a ship will ask whether Alexander still lives. If she is not assured by the crew that Alexander still lives and rules, she causes a storm to sink the ship and crew.
More photos and information on this sculpture can be seen here.