#### FIBONACCI SEQUENCE

Firstly, we were introduced to the 'Fibonacci Sequence' which is a geometric spiral made from quater circles. It has a ratio of 8:13 and no matter how large you make the spiral it will always have the same proportions, meaning that illustrator work can be created at a small scale using the Fibonacci spiral to keep in proportion. Then when the vectors are resized the proportions of the work stay the same, this is useful when creating illustrator work for bilboards and large signs.
http://upload.wikimedia.org/wikipedia/en/archive/7/79/20060826023537!Fibonacci_spiral.svg

We used our new found knowledge of Fibonacci's Sequence to create our own grid.

We used our new found knowledge of Fibonacci's Sequence to create our own grid.

The spiral can be found throught history, it was used by both the ancient Egyptians and Greeks. Moreover, the spiral can also be found within nature, in certain fruit and shells, human anatomy and Renaissance art. Paintings such as the Mona Lisa use sacred geometry to keep all elements of the body in proportion.

This tabel shows the equasion and how the next number is generated. If we add up the the two numbers before the answer, we get the next number in the sequence.

Moreover, the sequence can be written as a rule.

Firstly, the terms are numbered.

So, term 5 would be

^{X}5 and term 6 would be^{X}8.
The rule is written: x

_{n}= x_{n-1}+ x_{n-2}Therefore, if we wanted to find out term 10 in the sequence we would use;

^{X}10 =

^{x}10-1 +

^{x}10-2 =

^{x}9 +

^{x}8 = 34 + 21 = 55

http://www.mathsisfun.com/numbers/fibonacci-sequence.html

#### GOLDEN SECTION

Next, we were introduced to the 'Golden Section' otherwise known as the 'Golden Mean' which directly relates to the 'Fibonacci Sequence'. Much a like the Fibonacci Sequence it can be found throughout history in ancient civilizations.

The 'Golden Number' is approximately 1.62 and can be found by dividing numbers from the Fibonacci Sequence.

For an example I will divide terms 8 and 7.

21 / 13 = 1.61538.

Moreover, we can also use the 'Golden Number' to create grids to work on. Simply measure the edge of a piece of paper, and divide it by the golden mean. Use the number generated to measure to, mark this spot and draw a horisontal line.

Repeat this method, making sure that you always divide the longest edge to create a grid. I experimented with this method to create the grid shown below.

http://library.thinkquest.org/trio/TTQ05063/phibeauty3.htm

The 'Golden Number' is approximately 1.62 and can be found by dividing numbers from the Fibonacci Sequence.

For an example I will divide terms 8 and 7.

21 / 13 = 1.61538.

Moreover, we can also use the 'Golden Number' to create grids to work on. Simply measure the edge of a piece of paper, and divide it by the golden mean. Use the number generated to measure to, mark this spot and draw a horisontal line.

Repeat this method, making sure that you always divide the longest edge to create a grid. I experimented with this method to create the grid shown below.

http://library.thinkquest.org/trio/TTQ05063/phibeauty3.htm

#### THE RULE OF THIRDS

The concept of the golden ration can be simplified by using a slightly different technique. The rule of thirds governs the placement of points of interest.

Used in photography the rule of thirds is simple. Firstly, divide the image into thirds both ways (portrait/landscape)

Due to how the human brain works, the eyes are always attracted to the center of the page, meaning that the most important information should be placed centrally in the grid. Other important information should be placed on the information points which can be found where the lines intercept one and other.

http://www.mac-on-campus.com/Portals/0/Composition_and_Posing/MOC%20Zuckerman%20on%20Composition%20Rule%20of%20Thirds%201-1.jpg

After we finished learning about each rule we used magazine pages and ripped them up into the different grids that they were using. This exercise was useful as it allowed us to physically see the rules at work.

This page fit perfectly into the 'Rule of Thirds' rule.

Furthermore, I was also able to divide the page again horizontally.

This page used the 'Golden Ratio' rule to create its grid.

#### TASK

At the end of the session we were asked to create an interesting page size using the rules of the golden ratio to do this.

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