1. The introduction:
Hello my name is Frederick Smith, I will be speaking you about a fascinating thing that is in everything, it’s a part of you, it created you & its not just in you, its all around you. Its also in all plants and in all animals. Take for example an octopus has eight tentacles hence the name “octo’~pus, each one of its tentacles has the exact number of suckers on it and each tentacle is the same length pretty amazing right... (Pause for a break…) and the intricate design on a butterfly. One wing as the exact pattern as the other side in the exact spot adjacent to its counterpart (the other wing) It is exactly the same on one side as it is on the other? Or How does a seashell create a perfect spiral? so how does all this happen… (Another pause…) 2. Thesis statement
In nature there is something not visible bi the untrained eye. It happens because there is something in nature called the golden ratio. (Say softly & clearly…). Think of golden ratio as natures secret un~seen Architect! Although I am not a fan of mathematics, it’s in everything around you (Pause for break, let them think about it for a second)
Have any of you heard about the golden ratio before?
Other names frequently used for the golden ratio are the golden section and golden mean. Other terms encountered include extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, golden number, 2.1 History
Who came up with this, well it was a mathematician who also liked art, his name was Fibonacci, also known as Leonardo Pisano Bo Gallo he discover a sequence of numbers called the Fibonacci sequence if you take those numbers and u do some math they have a common mean 1.68 , hence the name golden mean, from this mean and number sequence the Fibonacci square is completed using te golden mean as its ratio, what’s cool about this square is if u take the height and fold it down back up ...
...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 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...
...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, 15711630
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 (490430 BCE). He produced the famous statue of Zeus in the...
...sequence 
Christos Vassos

Introduction
In this investigation we are going to examine the Fibonacci sequence and investigate some of its aspects by forming conjectures and trying to prove them. Finally, we are going to reach a conclusion about the conjectures we have previously established.
Segment 1: The Fibonacci sequence
The Fibonacci sequence can be defined as the following recursive function:
Fn=un1+ un2
Where F0=0 and F1=1
Using the above we can...
...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...
...The History of Algebra and
The GoldenRatio 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...
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