Have you ever found the answer to this question?
I have no idea if there is an authoritative answer to the question so I'll give my non-authoritative one.
There is little direct evidence that Masonry emerged from the Knights Templar. Many would like it to be true but the link is speculative. Maybe we can call ourselves the spiritual children. Godchild or stepchild maybe.
One of the symbols used in Masonry is the 47th problem of Euclid. It is also called the Pythagorean Theorem. Pythagoras was the first to prove that the sum of the squares on a right triangle is the square on the hypotenuse.
The public symbol of Masonry is the square and compasses. In high school geometry we learn to make a square using a compass. With the 47th problem we learn an additional way to make a square.
Lodge - Be there *and* be square.