After a Freemason has served a term as Worshipful Master and has installed his successor, he becomes the Immediate Past Master, commonly referred to as the IPM.
Whilst the IPM is not an Officer of the Lodge, it is a status afforded to him by virtue of his previous tenure as Worshipful Master. The IPM is there to offer support and advice to the new Master, and often has a small ceremonial role within the Lodge.
The collar jewel of a Past Master combines the Mason's square (the emblem of an Installed Master) with a representation of the 47th Proposition of Euclid, commonly known as Pythagoras' Theorem. This important piece of geometry is actually considerable older than Pythagoras, having been known to the ancient Babylonians a millennium earlier. As every good schoolboy and schoolgirl will tell you, the Theorem describes the unique and perfect relationship between the sides of all right-angled triangles.
It is unclear why this specific symbol was chosen to represent a Past Master but, as Pythagoras' Theorem helps us discover knowledge of our universe and describes a perfect "square" relationship, perhaps it is symbolic of the IPM's considerable knowledge of Freemasonry. There are many other interesting theories on this matter.
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