Leonardo Fibonacci (c. 1170-c. 1250)
Leonardo Fibonacci, also called Leonardo of Pisa, was believed the greatest mathematician of the Middle Ages. His Liber Abaci ('The Book of Calculation', 1202) introduced the Arabic system of numerals that originated in India to Europe.The book illustrated the virtues of the new numeric system showing how it can be used to simplify highly complex calculations. It included work on geometry, the theory of proportion and techniques for determining the roots of mathematical equations.
Fibonacci Numbers
Fibonacci discovered what we know now as Fibonacci numbers or Fibonacci sequence. Mathematics students and gurus of this branch of science will remember the famous numbering sequence of Fibonacci: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on up the line, in which the two previous numbers in the series add up to the next one or equal to the sum of the preceeding two integers.Relationship of Fibonacci Numbers to the Golden Ratio
Dividing any number in the series by its predecessor - for example, 8 divided by 5 or 13 divided by 8 - invariably will yield something around 1.6. This is called the "golden ratio" found in nature.
The Golden Ratio
Apparently, the bigger the pair of Fibonacci Numbers, the closer the approximation. Trying a few
A
|
B
|
B/A (Golden Ratio) | |||||
|---|---|---|---|---|---|---|---|
2
|
3
|
1.5 | |||||
3
|
5
|
1.666666666... | |||||
5
|
8
|
1.6 | |||||
8
|
13
|
1.625 | |||||
...
|
...
| ... | |||||
144
|
233
|
1.618055556... | |||||
233
|
377
|
1.618025751... | |||||
...
|
...
|
... |
The Golden Ratio (symbol is the 21st Greek alphabet letter "phi") is a special number approximately equal to 1.618. Since the digits just keep going with no pattern, we can infer that the Golden Ratio is equal to:
1.61803398874989484820... (etc.)
The Golden Ratio is also sometimes called the golden number, golden mean, golden section, golden proportion, divine proportion and divine section.
The Golden Ratio appears many times in geometry, art, architecture and other areas where designing is involved.
You can read my short article written for Decoded Science entitled "The Fibonacci Series in Phi Shapes and Numbers: Sacred Geometry in Nature and Culture" dated September 23, 2011.
Leonardo Fibonacci image:
Monument of Leonardo da Pisa (Fibonacci), by Giovanni Paganucci, completed in 1863, in the Camposanto di Pisa.
Resources:
The Designer's Guide to the Golden Ratio. Creative Bloq
The Golden Ratio. geom.uiuc.edu.
The Golden Ratio. Golden.Number.net
The Parthenon and Phi, The Golden Ratio.
What is the Golden Ratio. Live Science
Originally published May 13, 2012, updated 10 August 2016.
(c) Tel Asiado, written for InspiredPenWeb.com. All rights reserved.
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