Fibonacci Forgot the Number Squares

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.

F1F2F3F4F5F6F7F8F9F10F11F12F13F14F15F16F17F18F19F20
11235813213455891442333776109871597258441816765

Fibonacci forgot the number squares behind the series
Actual squares with Fibonacci numbers

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.

1st sentence of Genesis Archives – DSO Works

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.

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