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.
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,