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〃You do？〃
〃Yup。 PHI。〃
The girl gaped。 〃NO WAY！〃
〃Way！〃 Langdon fired back； smiling as he projected a slide of a spiral seashell。 〃Recognize this？〃
〃It's a nautilus；〃 the bio major said。 〃A cephalopod mollusk that pumps gas into its chambered shell to adjust its buoyancy。〃
〃Correct。 And can you guess what the ratio is of each spiral's diameter to the next？〃
The girl looked uncertain as she eyed the concentric arcs of the nautilus spiral。
Langdon nodded。 〃PHI。 The Divine Proportion。 One…point…six…one…eight to one。〃
The girl looked amazed。
Langdon advanced to the next slide—a close…up of a sunflower's seed head。 〃Sunflower seeds grow in opposing spirals。 Can you guess the ratio of each rotation's diameter to the next？〃
〃PHI？〃 everyone said。
〃Bingo。〃 Langdon began racing through slides now—spiraled pinecone petals； leaf arrangement on plant stalks； insect segmentation—all displaying astonishing obedience to the Divine Proportion。
〃This is amazing！〃 someone cried out。
〃Yeah；〃 someone else said； 〃but what does it have to do with art？〃
〃Aha！〃 Langdon said。 〃Glad you asked。〃 He pulled up another slide—a pale yellow parchment displaying Leonardo da Vinci's famous male nude—The Vitruvian Man—named for Marcus Vitruvius； the brilliant Roman architect who praised the Divine Proportion in his text De Architectura。
〃Nobody understood better than Da Vinci the divine structure of the human body。 Da Vinci actually exhumed corpses to measure the exact proportions of human bone structure。 He was the first to show that the human body is literally made of building blocks whose proportional ratios always equal PHI。〃
Everyone in class gave him a dubious look。
〃Don't believe me？〃 Langdon challenged。 〃Next time you're in the shower； take a tape measure。〃
A couple of football players snickered。
〃Not just you insecure jocks；〃 Langdon prompted。 〃All of you。 Guys and girls。 Try it。 Measure the distance from the tip of your head to the floor。 Then divide that by the distance from your belly button to the floor。 Guess what number you get。〃
〃Not PHI！〃 one of the jocks blurted out in disbelief。
〃Yes； PHI；〃 Langdon replied。 〃One…point…six…one…eight。 Want another example？ Measure the distance from your shoulder to your fingertips； and then divide it by the distance from your elbow to your fingertips。 PHI again。 Another？ Hip to floor divided by knee to floor。 PHI again。 Finger joints。 Toes。 Spinal divisions。 PHI。 PHI。 PHI。 My friends； each of you is a walking tribute to the Divine Proportion。〃
Even in the darkness； Langdon could see they were all astounded。 He felt a familiar warmth inside。 This is why he taught。 〃My friends； as you can see； the chaos of the world has an underlying order。 When the ancients discovered PHI； they were certain they had stumbled across God's building block for the world； and they worshipped Nature because of that。 And one can understand why。 God's hand is evident in Nature； and even to this day there exist pagan； Mother Earth…revering religions。 Many of us celebrate nature the way the pagans did； and don't even know it。 May Day is a perfect example； the celebration of spring。。。 the earth ing back to life to produce her bounty。 The mysterious magic inherent in the Divine Proportion was written at the beginning of time。 Man is simply playing by Nature's rules； and because art is man's attempt to imitate the beauty of the Creator's hand； you can imagine we might be seeing a lot of instances of the Divine Proportion in art this semester。〃
Over the next half hour； Langdon showed them slides of artwork by Michelangelo； Albrecht Dürer； Da Vinci； and many others； demonstrating each artist's intentional and rigorous adherence to the Divine Proportion in the layout of his positions。 Langdon unveiled PHI in the architectural dimensions of the Greek Parthenon； the pyramids of Egypt； and even the United Nations Building in New York。 PHI appeared in the organizational structures of Mozart's sonatas； Beethoven's Fifth Symphony； as well as the works of Bartók； Debussy； and Schubert。 The number PHI； Langdon told them； was even used by Stradivarius to calculate the exact placement of the f…holes in the construction of his famous violins。
〃In closing；〃 Langdon said； walking to the chalkboard； 〃we return to symbols〃 He drew five intersecting lines that formed a five…pointed star。 〃This symbol is one of the most powerful images you will see this term。 Formally known as a pentagram—or pentacle； as the ancients called it—this symbol is considered both divine and magical by many cultures。 Can anyone tell me why that might be？〃
Stettner； the math major； raised his hand。 〃Because if you draw a pentagram； the lines automatically divide themselves into segments according to the Divine Proportion。〃
Langdon gave the kid a proud nod。 〃Nice job。 Yes； the ratios of line segments in a pentacle all equal PHI； making this symbol the ultimate expression of the Divine Proportion。 For this reason； the five…pointed star has always been the symbol for beauty and perfection associated with the goddess and the sacred feminine。〃
The girls in class beamed。
〃One note； folks。 We've only touched on Da Vinci today； but we'll be seeing a lot more of him this semester。 Leonardo was a well…documented devotee of the ancient ways of the goddess。 Tomorrow； I'll show you his fresco The Last Supper； which is one of the most astonishing tributes to the sacred feminine you will ever see。〃
〃You're kidding； right？〃 somebody said。 〃I thought The Last Supper was about Jesus！〃
Langdon winked。 〃There are symbols hidden in places you would never imagine。〃
〃e on；〃 Sophie whispered。 〃What's wrong？ We're almost there。 Hurry！〃
Langdon glanced up； feeling himself return from faraway thoughts。 He realized he was standing at a dead stop on the stairs； paralyzed by sudden revelation。
O； Draconian devil！ Oh； lame saint！
Sophie was looking back at him。
It can't be that simple； Langdon thought。
But he knew of course that it was。
There in the bowels of the Louvre。。。 with images of PHI and Da Vinci swirling through his mind； Robert Langdon suddenly and unexpectedly deciphered Saunière's code。
〃O； Draconian devil！〃 he said。 〃Oh； lame saint！ It's the simplest kind of code！〃
Sophie was stopped on the stairs below him； staring up in confusion。 A code？ She had been pondering the words all night and had not seen a code。 Especially a simple one。
〃You said it yourself。〃 Langdon's voice reverberated with excitement。 〃Fibonacci numbers only have meaning in their proper order。 Otherwise they're mathematical gibberish。〃
Sophie had no idea what he was talking about。 The Fibonacci numbers？ She was certain they had been intended as nothing more than a means to get the Cryptography Department involved tonight。 They have another purpose？ She plunged her hand into her pocket and pulled out the printout； studying her grandfather's message again。
13…3…2…21…1…1…8…5
O； Draconian devil！
Oh； lame saint！
What about the numbers？
〃The scrambled Fibonacci sequence is a clue；〃 Langdon said； taking the printout。 〃The numbers are a hint as to how to decipher the rest of the message。 He wrote the sequence out of order to tell us to apply the same concept to the text。 O； Draconian de