what makes the different shapes of the moon
Lunar phase The lunar phase or phase of the moon is the shape of the illuminated (sunlit) portion of the Moon as seen by an observer on Earth. The lunar phases change cyclically as the Moon orbits the Earth, according to the changing positions of the Moon and Sun relative to the Earth. The Moon's rotation is tidally locked by the Earth's gravity, therefore the same lunar surface always faces Earth. This face is variously sunlit depending on the position of the Moon in its orbit. Therefore, the portion of this hemisphere that is visible to an observer on Earth can vary from about 100% (full moon) to 0% (new moon). The lunar terminator is the boundary between the illuminated and darkened hemispheres. Each of the four "intermediate" lunar phases (see below) is roughly seven days (~7.4 days) but this varies slightly due to the elliptical shape of the Moon's orbit. Aside from some craters near the lunar poles such as Shoemaker, all parts of the Moon see around 14.77 days of sunlight, followed by 14.77 days of "night". (The side of the Moon facing away from the Earth is sometimes called the "dark side of the Moon", although that is a misnomer.)
Crescent The crescent shape consists of a circular disk with a segment of another circle removed from its edge, so that what remains is a shape enclosed by two circular arcs of different diameters which intersect at two points (usually in such a manner that the enclosed shape does not include the center of the original circle). As such, it belongs to the class of figures known as lune in planar geometry. The tapering towards the points of intersection of the two arcs are known as the "horns" of the crescent. The classical crescent shape has its horns pointing upward (and is often worn as horns when worn as a crown or diadem, e.g. in depictions of the lunar goddess, or in the headdress of Persian kings, etc.[7]