Why does a Hanukkah menorah have nine branches?

The Hanukkah menorah, also known as a hanukkiyah, features nine branches to commemorate the miracle of the oil associated with the rededication of the Second Temple in 164 BCE.12

According to the Babylonian Talmud, when the Maccabees reclaimed the Temple, they found only enough consecrated oil to light the menorah for one day, yet it miraculously burned for eight days. To represent this eight-day miracle, the hanukkiyah includes eight receptacles for candles or oil. The ninth branch holds the shammash, or "servant" light, which is set apart—often elevated—and used to kindle the other eight lights during the nightly ritual.2314