Decrypting the DA VINCI CODE further…

Read “Da Vinci Code”?

Remember “Fibonacci Sequence” and “PHI”? Used to indicate that “O, Draconian Devil” was actually “Leonardo Da Vinci” and “Oh, Lame Saint” was “The Mona Lisa”. That was just an anagram. Changing the places of letters in a phrase you obtain some other phrase. But, that’s not our today’s topic of discussion. I have something more stunning for you today.

Let me show you some interesting mathematical properties of “Fibonacci Sequence” and “PHI” that I found. (Thanks to my CASIO – 82 FX calculator)

But before that, let us refresh our memories. A sequence where a number is obtained by adding two previous numbers is a “Fibonacci Sequence”. Here it is…

1 – 1 – 2 – 3 – 5 – 8 – 13 – 21 – 34 – 55 – 89 – 144 – 233- 377 – 610 – 987 - ….

PHI (not to be confused with PI) is a Magic number with value, up to 3 digits is 1.618. Its actual value when I calculated was… 1. 6180399 (Shame on my CASIO – 82 FX calculator that displays only 8 digits)

Why it is called a Magic number? And how it is related to “Fibonacci Sequence”?

Dan Brown, a brilliant mind, has explained one mathematical relation in his “Da Vinci Code”. Take any two sequential numbers, and there quotient (division of bigger by smaller) tends to “PHI”. ( 987 / 610 = 1.6180328) Dan Brown tells us some other reasons mostly related to nature and art to explain why it’s a magic number. (like ratio of diameters of sequential circles on a sea shell is also equals to PHI etc.)

Mind you, these are not the only reasons why PHI is called magic number. Come along, I have found some very interesting mathematical stuff for you.

1. PHI * PHI = PHI + 1.
What is square of PHI, It’s 2.16180399. There are some other stunning features. Just go on.

2. 1/ PHI = PHI -1
You know what is 1 / PHI i.e. 1 / 1.6180399? It’s 0.6180399 again. Isn’t it surprising? In fact I would say rather than 1.6180399, 0.6180399 is a Magic number. You will also agree me after some time.


3. Fibonacci Sequence Quotients
Leave one number in between and take quotients.
987 / 377 or 610 / 233. The answer tends to 2.6180399.
The answer is square or second power of PHI.

Now, Leave two numbers in between and take quotients.
987 / 233 or 610 / 144. The answer tends to 4.236068
The answer is cube or third power of PHI.

And try some more. You will find quotient is equal to PHI raise to numbers left in between plus one. What you say about it?


4. My method of synthesizing PHI –
Keep your scientific calculator ready or you will need to write a few lines of code to feed into your compiler.

Take any number. Any positive real number. Let us take 50.50. Let us name it “x”. Find out 1/x and add 1 to that. Now make new obtained number “x” and repeat the cycle. After some cycles you will find that “x” tends to PHI. Initial number could be any thing but you will get PHI at the end. Here is code snippet for the same. Add appropriate breaks to the infinite loop.

x= 123.45;
for(;;)
x= (1/x)+1;


When you will print “x”, you will find that it’s nothing else but our very magical PHI again.

Well, can you guess why the synthesized number and PHI are one and the same? Tell me on vikram.aphale@gmail.com

THERE WILL BE LOT ABOUT SERIES AND SEQUENCES IN COMING ARTICALS. KEEP VISITING THE SAME BLOG. BYE BYE.