Why isn the quarter moon called a half moon?
The terms first quarter and last quarter refer not to the moon’s apparent shape but to the points in time within the lunar month. We recognize four main phases, and therefore divide the lunar cycle into 4 parts, or quarters. Starting with new moon, then first quarter, full, then last quarter, then back to new. For each of the 4 main phases, the moon has orbited one quarter of the way around the earth.