quarter moon

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quarter moon (plural quarter moons)

1. (astronomy) Either of the intermediate stages between the new and full moons.

   Synonyms: half-moon, quarternary moon

In spite of the name, half of the Moon's visible portion is lit up during a quarter moon, hence, it is also called a half-moon. It is called quarter moon because it is at 1/4^th or 3/4^th of the way of the cycle from one new moon to the next new moon (which is called a “lunar month” or “moon” for short, hence the “quarter moon” designation.)