Fibonacci Five

So what’s so special about Fibonacci five? Here are its beginning numbers in order of appearance in this numerical series that continues to infinity. Each number becomes the sum total of the previous two numbers after number one is repeated. Remember number “one” appears twice: We have 1,1,2,3,5,8,13,21,55, 89, 144, 233, 377, 610, 987…etc. Five breaks the pattern of the consecutive numbers 1,2,3.

Look at the perimeter of the magic 3 x 3 square overlapping two numbers in opposite directions around perimeter-2 as follows: 49 + 92 + 27 + 76 + 61 + 18 + 83 + 34 = 440. Now going in reverse we still get 440. : 43 + 38 + 81 + 16 + 67 + 72 + 29 + 94 = 440. Very important, with eight sets of numbers the average becomes 55. Four hundred and forty still has two more ways to be found. Future posts deal with this issue. By single numbers, perimeter one is simple 40. Here the average of each set is “5”. Finally, triple numbers overlapping the corner numbers yields 2,220. (492 + 276 + 618 + 834 = 2220). With these four sets of numbers the average is five hundred and fifty-five.

Let us take another look at how the three by three magic square and Fibonacci series correspond:

1. By the single digit, five, we find it as the core of the 3 x 3 magic square.
2. By double digits, 55 (another Fibonacci number) becomes an average of two numbers at the time on this magic square.
3. That seems to be as far as we can go; but consider this: The average of three numbers at the times becomes five hundred and fifty-five. For example, 2,220/4 = 555. That is not a Fibonacci number by itself. However, 55 + 555 = 610!!!