Crescent vs Castor

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A crescent shape (, British English also ) is a symbol or emblem used to represent the lunar phase in the first quarter (the "sickle moon"), or by extension a symbol representing the Moon itself. In Hinduism, Lord Shiva is often shown wearing a crescent moon on his head symbolising that the lord is the master of time and is himself timeless. It is used as the astrological symbol for the Moon, and hence as the alchemical symbol for silver.

It was also the emblem of Diana/Artemis, and hence represented virginity. In Roman Catholic Marian veneration, it is associated with the Virgin Mary. From its use as roof finial in Ottoman era mosques, it has also become associated with Islam, and the crescent was introduced as chaplain badge for Muslim chaplains in the US military in 1993.

Source: Wikipedia