Who knows why the Moon box is called the Moon box?

Who knows why the Moon box is called the Moon box. Always getting asked this by clients. I assumed a quick google search would reveal the answer, but 30 mins later still none the wiser. How bizarre! Somebody here must know!!

Just heard this during the past year: because the box 'orbits' around the Mat! Cool, huh? 

Disclaimer: I don't know that this is the answer, but I found this when I tried to get wiser on the subject.  There's an item called "moon box" in the world of space aviation that has an uncanny resemblance with the shape of the original "moon boxes" in the Pilates studio. I wouldn't be surprised if someone in the late 60s picked up on the similarity and the moniker was born.