# PG Dip, Drawing 2002

During my BA years, I have tried to investigate a system where from looking at one thing can led me into many possibility.  But from looking at it in such a subjective point of view it became not so much of a system but confusion to the audiences and I, so I decided to start all over again.

Concentrating on No. 17: Sq No. 17 is a drawing that I have made from the system where I first drawn: No. 17 is also the drawing that I concentrating on devolving: In the diagram above I have tried to court the shape that excite in drawing No.17 but have found a lot of difficulties.

Taking No.17 as a drawing, it has 3 lines that are not completed so there is shapes that cannot be count because it dose not excite.  In the possibility of the 3 lines can then be drawn.  This shows below: Then this led me into a deeper investigation by taking to account everything start from the very beginning, simplicity “The Line” and “the Square”.
“The Line” is where I start my journey of make a drawing until the end.

A line is made up of 2 points.
A line can be drawn straight or cured.
A line consists of breadth, length and depth.
When a thick line is drawn, seeing it as 3D line, it becomes a big circle like a rod.
When a thin line is drawn, seeing it as a 3D line, it will look like a pin that are hardly to be seen.

“The Square” is the shape I have chosen for most of my drawing as a frame for the chose of composition of my work.

A square consists of 4 lines in the same length.
A square consists of 4 points in the same distance.
By joining the 4 points together using the 4 lines will draw the square.

Taking these 2 things, I started my investigation on how many lines are entered into the square may affect on have many shapes may appear, and how dose it work?

The first line entered into the square we have 3 shapes! The 2nd line entered into the square we have 7 shapes! The 3rd line entered into the square we have 15 shapes! The 4th line entered into the square we have 27 shapes! The 5th line entered into the square we have 43 shapes! From looking at these there is a clear sequence that is happening here, look at the chat below:

No. of lines:                0,    1,    2,    3,    4,    5…
No. of shapes:                1,    3,    7,    15,    27,    43…
No. of difference when line increase:    1,    +2,    +4,    +8,    +12,    +16…

Although this chat tells me there is a sequence, I was unable to find out what it really is so I decided I had to study into mathematic. Than by researching into the topic, I have at last come to a mathematic term called “the sum of arithmetic progression” [L. Btock and S.Chandler, 1994. pp 640] which very much become the conclusion.

Because this equation only can find out the number of terms times the average term from the number starting from 0, I have to then put into the equation that we do not start from 0 but a square which will be The number of lines –3 at the end of the equation.  Which becomes this:

Here is an example:

The sequence     =    5/2 [2 x 1 + (5 – 1) x 4] – (5 – 3)
=    2.5 [2 + 4 x 4] – 2
=    [2.5 x 18] –2
=    45 – 2
=    43

The above example is from 5 lines into the square that will then give us the conclusion of 43 shapes that excite in that drawing.

This project continued from going back to the 1st sequence where I have found out when 1 line is entered into a square equal 3 shapes.  For the 3 shape to be placed there will than be many possibilities and this is influence from Sol LeWitt [LeWitt, Sol, 1973 The Location of lines] In this book, it go in depth in how the placing of the line then affect the ways in how we visually read the line to the relation of the frame itself.

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