Tabularization of the Fibonacci Series
Most of the numerical tables that will be presented at this site and at various other sites on the internet by the author result from a combination of two well-known mathematical procedures.
- The Numerical reduction of multi-digit numbers by digit addition to form a single digit. This process to produce single digit numbers is referred to by this author as distillation. It is also known as "The casting out of nines".
- The Fibonacci number series is created by starting with (1) and adding it to zero, that produces another (1). Each number of the ‘series’ is thus formed from the sum of the two previous numbers. This string of numbers will increase infinitely unless the distillation process is applied. When distilled, the new number set is limited to a 24 digit string that will duplicate itself repeatedly if the summation process is continued. i.e.
(Fibonacci series) Þ 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ¼ ¥
(Distilled values) Þ 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, ¼ 9.
It is this first 24 digit string that is used to create Row-one of all tables.
The
distilled Fibonacci numbers and the distilled multiples thereof are used to form 9 horizontal rows, each containing 24 digits. Continuation of the rows beyond 24 digits merely reproduces the original digit string. Likewise, continuation of the row multiples beyond nine only reproduces each original row. (see Table-1 below)
The tables are shown with differing shades of gray to simplify discussion of table summation processes. Column and row sums are generally displayed in white cells along the border of the tables.
It should be noted that only the series numbers displayed in the gray shaded portions of the tables were obtained by distillation.
In Table-1, the distilled Fibonacci numbers each occupy a cell, which produces a horizontal cell count of twenty-four.
In Table-2, (not shown here) the distilled series digits are placed two to a cell in their original order thereby reducing the horizontal cell count to twelve. These two digits are now treated as double-digit numbers for the column and row summations.
A similar row reduction to eight cells occurs for Table-3 where three sequential series digits occupy each cell and are treated as triple digit numbers when summing.
The tables and sub-tables to be presented on occasion at this website display a surprising amount of symmetry, both numerical and graphical, as might be expected by such a modification of Leonardo Fibonacci’s mathematical series that was first reported in the 13
th century.
Important Note:
All tables created and discussed by the author, in the various articles presented on the internet and in his books, provide no units for the chosen summation numbers. This only causes one to assume it is self-evident, that in order to have any meaning, the unit for such numbers have to be one of those that is found in the British Imperial system of units, e.g. (mile, foot. inch, etc.) In other words, no correlation effects are apparent if summation units are assumed to be in metric units.
Table-1 Notes from Column, Row and Specific Area Sums
- Baseline Width (feet) of the Great Pyramid = 1188 – 2(216) = 4 (189) = 756 feet.
- The total sum minus the sum of all the nines = 1188 - 9(48) = 1188 – 432 = 756 feet.
- The digit sum of the two central squares = 216 Þ Also, 216 is the number of table
cells.
- The sum of the perimeter digits (light gray cells) = 612 Þ Apothem length = 612 feet.
- The sum of the forty border nines (dark gray cells) = 9(40) = 360 Þ 360 degrees
- Great Pyramid scale size to the Earth = (1 : 43200) Þ 2(216) = 432 = Base ten factor.
- Pyramid Pi Factor (pp) = 594 ÷ 189 = 22/7 = 3.142857
- Pyramid’s Height = Base Area Circumference ÷ 2pp = (4 x 756 ft) ÷ 2(22/7) = 481.1 feet
- Pyramid’s Height = Base Area ÷ Total Sum of Table-1 = (756 ft)2 ÷ 1188 ft = 481.1 feet
- Time note (see column sums): (189,216,000 sec.) ÷ (86400 sec/day) ÷ (365 day/yr.) º 6 yr.
- Time note (see column sums): (378,432,000 sec.) ÷ (86400 sec/day) ÷ (365 day/yr.) º 12 yr.
- Time note (see column sums): (756,864,000 sec.) ÷ (86400 sec/day) ÷ (365 day/yr.) º 24 yr.
Ó 1999, Joseph Turbeville - All rights reserved
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