The History of Algebra and
The Golden Ratio in Nature

By: Lauren Pressley
Introduction to Statistics

Throughout history algebra has changed in words through etymology. Etymology is an account of the history of a particular word or elements of a word. The word “algebra” is derived from Arabic writers. Algebra is a method for finding solutions of equations to the simplest possible form. Different cultures have come up with different types of names to classify algebra. Al Khwarizmi and Fibonacci contributed talented mathematic systems that shaped algebra. Al Khwarizmi was born in the town of Khwarizm in Khorason. He achieved most of his work between 813 a.d and 833 a.d. Khwarizmi contributed logical approaches to algebra and trigonometry. He came up with ways of solving linear and quadratic equations. Khwarizmi was not the only person who contributed to algebra; Fibonacci contributed to algebra has well. one by adding a number to sum up the two numbers that precedes the previous two numbers. He used this method to tie nature and mathematic together. It is formed by using a triangle whose sides’ measure one number of the Fibonacci

Fibonacci contributed the decimal number system which is known as the Fibonacci sequence. The Fibonacci sequence is closely related to the golden ratio that uses the number number of the Fibonacci sequence. Fibonacci was born in Pisa, Italy around 1175. He studied mathematics in North Africa in the city of Bugia. Fibonacci’s greatest achievement was the golden ratio in nature. For example, plants grow new cells in spirals such as this pattern of seeds in a sunflower. The seeds in a sunflower are packed in going left and right making a spiral affect. The number of lines in the spiral of a sunflower is almost the numbers leading to the Fibonacci sequence.

The golden ratio is an irrational mathematic constant of 1.6180339887 found in nature. When...

...
The Golden Number
1.61803 39887 49894 84820 is by no means a number of memorization. However, it is a recognizable one. Never will you find a combination of numbers that is more significant than this one. This ratio is known as the Golden Number, or the GoldenRatio. This mystery number has been used throughout different aspects of life, such as art, architecture, and of course, mathematics. One may wonder where the...

...What is the GoldenRatio?
Most people are familiar with the number Pi because it can be found in so many different math problems and equations. There is, however, another irrational number like Pi. This number isn¡¦t as well known as Pi however. This number is called Phi. This number is also called the goldenratio. The goldenratio is equal to the square root of five plus one, divided by two. If you work...

...The GoldenRatio: Natures Beautiful Proportion
At first glance of the title, many may wonder: What is the GoldenRatio? There are many names the GoldenRatio has been called including the Golden Angle, the Golden Section, the Divine Proportion, the Golden Cut, the Golden Number et cetera, but what is it and how is it useful for society...

...Goldenratio ; The Definition of Beauty
“Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.” Johannes Kepler, 1571-1630
The goldenratio is present in everyday Life. The golden proportion is the ratio of the shorter length to...

...The GoldenRatio
By : Kaavya.K
In mathematics and the arts, two quantities are in the goldenratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The goldenratio is an irrational mathematical constant, approximately 1.6180339887. Other names frequently used for the...

...The GoldenRatio
Body, art, music, architecture, nature – all connected by a simple irrational number – the GoldenRatio. According to Posamentier & Lehmann in their work The
(Fabulous) Fibonacci Numbers, there is reason to believe that the letter φ (phi) was
used because it is the first letter of the name of the celebrated Greek sculptor Phidias (490-430 BCE). He produced the famous statue of Zeus in the...

...GoldenRatio
In mathematics, two quantities are in the goldenratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b,
Where the Greek letter phi (φ) represents the goldenratio. Its value is:
The...

...calculate the rest of the terms the same way:
F0 | F1 | F2 | F3 | F4 | F5 | F6 | F7 |
0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 |
Segment 2: The Goldenratio
In order to define the goldenratio we need to examine the following sketch:
The line above is divided into two segments in such a way that ABAP=APPB
The ratio described above is called the goldenratio.
If we assume that AP=x units...

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