# Fibonacci Forgot the Number Squares

Fibonacci Forgot the Number Squares. First, what are the Fibonacci numbers? The Fibonacci numbers are a sequence of numbers in mathematics named after Leonardo of Pisa.  Fibonacci wrote a book in 1202, called Liber Abaci (“Book of Calculation”). He introduced the number pattern to Western European mathematics.  Mathematicians in India already knew of it.[1][2]

Here we start with  #1.  This is because zero was not considered a number in the remote past.  In the more modern series, number one repeats. Each number after that is equal to adding the two numbers right before it together. For example, 1 + 1=2. Then 1 + 2 = 3. Next,  2 + 3 =5. Next, 3 + 5 = 8. This sequence can go on forever. Note: Five breaks the consecutive number series of 1,2,3. It skips number “4”. Therefore, I call five the 1st distinct Fibonacci number. It is also the first central number of the 1st number square of the series. It sits at the center of the 3 x 3 number square.

 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15 F16 F17 F18 F19 F20 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

This can be written as a recurrence relation,

A Fibonacci spiral created by drawing a line through the squares in the Fibonacci tiling. This one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34; see Golden spiral.

### What Fibonacci Forgot is Key to Understanding

We just mentioned the centrality of #5 in number squares. Number 13 is at the center of the 5 x 5 square. All evenly numbered squares have 4 numbers at the center. The 4 x 4 square is the 1st such square. Its 4 numbers of 7,6,10 and 11 total 34. This is yet another Fibonacci number that comes from the heart of number squares. The most remarkable is the 3 x 3 number square. It actually frames the infinite Fibonacci series by using repeated fives. Many blogs on DSOworks.com are about this very topic. Here are just two internal links.

### Tens: Here’s the Formula on How Tens Grow into Infinity – DSO Works

What Fibonacci forgot is the heart of the entire matter. It time to place some teeth into this prehistoric series of numbers. Numbers squares can be a guiding light to an uplifting future.