Shiva as Ardhanarishwar is half-woman half-man. Story of Sage Bhringi and Ardhariswar form of Shiva is found in Tamil culture. Legend has it that Sage Bhringi once went to Kailash to pay darshan to Shiva. He wanted to circumambulate Shiva.
But Goddess Parvati was always with Shiva and the sage was not ready to circumambulate Goddess Parvati.
Now Goddess Parvati was not ready to make way for the sage and She sat on the lap of Shiva. This made it impossible for the sage to circumambulate only Shiva.
Sage Bhringi then took the form of a bee to fly around the head of Shiva.
But Goddess Parvati merged with Shiva and the divine couple became Ardhanarishwar. This is believed to be the origin of Ardhanarishwar.
The legend continues… and it is said that the sage took the form a worm and entered the body of Ardhanarishwar and created hole and circumambulated only Shiva.
Goddess Parvati became furious and cursed Bhringi to loose his flesh and blood. The sage was reduced to a skeleton and could not stand or move
Shiva took pity on his devotee and gave him a third leg to stand upright.