The Golden Ratio, also known as The Divine Proportion, The Golden Mean, or Phi, is a constant that can be seen all throughout the mathematical world. This irrational number, Phi (? ) is equal to 1. 618 when rounded. It is described as “dividing a line in the extreme and mean ratio”. This means that when you divide segments of a line that always have a same quotient. When lines like these are divided, Phi is the quotient:

When the black line is 1. 18 (Phi) times larger than the blue line and the blue line is 1. 618 times larger than the red line, you are able to find Phi. What makes Phi such a mathematical phenomenon is how often it can be found in many different places and situations all over the world. It is seen in architecture, nature, Fibonacci numbers, and even more amazingly,the human body. Fibonacci Numbers have proven to be closely related to the Golden Ratio. They are a series of numbers discovered by Leonardo Fibonacci in 1175AD. In the Fibonacci Series, every number is the sum of the two before it.

The distance from a person’s head to their fingertips divided by the distance from that person’s head to their elbows equals Phi. (Jovanovic).

Because Phi is found in so many natural places, it is called the Divine ratio. It can be tested in a number of ways, and has been by various scientists and mathematicians. I have chosen to investigate the Phi constant and its appearance in the human body, to find the ratio in different sized people and see if my results match what is expected. The aim of this investigation is to find examples of the number 1. 618 in different people and investigate other places where Phi is found.

### The Essay on Number Line Stephanie Day Girl

When I arrived at the Mountain View Elementary school today, I never imagined it would be my most challenging day yet. Stephanie was indeed a very special young girl, but in more ways than one. Stephanie's teacher had informed me that the little girl was diagnosed with a learning disability, and although she was in the 3 rd grade, she worked on a kindergarten level. My task for the day was helping ...

Five people were measured and each participant had these parts measured: * Distance from head to foot * Distance from head to fingertips * Length of lowest section of index finger * Length of middle section of index finger * Distance from elbow to fingertips * Distance from wrist to fingertips The ratios were found, to see how close their quotients are to Phi (1. 618).

Then the percentage difference was found for each result.