As they creep towards their exit, Langdon's trying to piece together what he knows. He's still puzzled as to why Fache is trying to frame him for Saunière's murder, and why Saunière would want Sophie to find him.
Sophie reassures Langdon that everything in her grandfather's message was meant to get her attention.
The pentacle used to be an inside joke between them from when they used to play Tarot.
The Fibonacci sequence, his body arrangement, and the fact that he wrote the message in English was all like "waving a flag".
Langdon asks if her grandfather had ever mentioned goddess worship or anything like that to her when he had explained the pentacle. She says she was more interested in the mathematics of it, and PHI, the Divine Proportion: 1.618.
Langdon, the nerd that he is, flashes back to his classes he has taught on PHI (pronounced "fee").
There are several nerdy puns about PHI. (We approve.)
The number PHI was derived from the Fibonacci sequence: the quotients of adjacent terms all approach the number 1.618.
What makes PHI even cooler is that it is a fundamental building block in nature.
You find it everywhere. (Watch this. Seriously. Walt Disney knew his stuff.)
Apparently, Da Vinci's Vitruvian Man was a tribute to the architect Marcus Vitruvius who had made the Divine Proportion in architecture just about ubiquitous; and showed the same proportion as applied to the human body.
Langdon lectures about how the pentacle is so powerful because the lines automatically divide themselves into segments according to the Divine Proportion, making it the ultimate expression of PHI.
All this reminiscing about his lecture has led to a breakthrough. He realizes what Saunière's code is referring to.
The code is actually an anagram. "O, Draconian devil! Oh, lame saint!" is a perfect scrambling of "Leonardo da Vinci! The Mona Lisa!"