“ Mom, did you say Grandpa was a cryptologist for the Indian army?” asked Deepak.
“ Do you even know what that means?” asked his mom Meera.
“They decipher coded messages,” said Tarun, Deepak’s twin brother.
“ Wow! My twelve year old twins sure are smart.”
“ Mom! Why is Grandpa’s room always locked? Dad never allows anyone inside. Is it because grandpa’s ghost is still inside?” Deepak chuckled.
“ Ha ha! I think it’s time I tell you both the secret,” exclaimed Meera.
“Please, tell us,” pleaded the twins.
“Well! There is actually a locker inside the room with treasure hidden. However, it’s not easy to get the code which is a two digit number required to open the lock.”
“Just try all possible combinations,” said Tarun.
“ No! That’s the catch. Only one attempt is allowed. If you fail, all the contents inside will get destroyed. There is a paper containing a riddle inside the room. Solving the riddle will reveal the code. The clues are also inside the room. Your dad has been breaking his head to solve the riddle ever since with no luck.”
“ Hmm! Show us the riddle. We’ll try.”
Meera unlocked Grandpa’s room and the twins entered. She gave them the paper.
The pictures speak,
The numbers count,
Find the relation without a doubt,
In one try, crack the secret code,
Else the ‘golden’ treasure will explode..
“ A strange riddle. Tarun, let’s do it bro,” said Deepak.
The first thing that caught their eyes were three large pictures of – pinecones, nautilus sea shells and pineapples.
“ I wonder why he chose these pictures? These could be clues. The riddle says – the pictures speak. Think, think,” said Deepak.
By then the twins’ father entered the room
“ Hey Deepak ! I just noticed. There are exactly nine shirts, nine pants and nine shoes in the cupboard,” said Tarun.
“ And nine books in the bookshelf, nine pens in the penholder.”
“ So the number nine must be a clue,” said their dad.
“ Dad , you are a botanist. Is there anything uniquely common about pine cones,nautilus sea shells and pineapples ?” questioned Deepak.
“ And the last line in the riddle has the word golden in quotes,” interrupted Tarun.
“ Bingo ! The golden ratio is prevalent in their structures.You guys are awesome,” said their Dad.
“The golden ratio?” The twins looked puzzled.
“When a fibonacci number is divided by a preceding fibonacci number it is called the golden ratio. In a fibonacci sequence each number is the sum of the preceding two numbers.”
“ Wow! So how do we relate nine with it ?”
“ The secret code is a two digit number though.”
They thought for a while.
“ What if it’s the ninth number in the sequence?” asked Tarun.
“ Hurray! Ninth number in the sequence. It is twenty one. That’s it,” said their dad as he keyed in the number.
The locker opened.
But to their dismay there was a map inside with a riddle, yet again.
“ Oh No! Not again,” they all exclaimed together.
The Famous Fibonacci
Often called ‘Nature’s Universal Rule’, the Fibonacci sequence is perhaps one of the most famous mathematical sequences. The origin of this sequence attributed to the Italian mathematician Leonardo Fibonacci.
In this sequence, each number is the sum of the two numbers that precede it. Take a look:
Something strange happens when the sequence approaches infinity. The ratio between two consecutive numbers converges to 1.61803… : ‘phi’, or as you might call it, the ‘golden ratio’.
Fibonacci Sequence in Nature
The Fibonacci sequence can be observed in a stunning variety of phenomena in nature.
Nautilus shells, one of the most iconic examples of the Fibonacci sequence, follow the proportional increase of 1.61.
The total number of petals of a flower is often a number present in the Fibonacci sequence, as with irises and lilies. Most pineapples have either five, eight, thirteen or twenty-one spirals; these are also Fibonacci numbers.