Introduction

There's something very appealing about the Golden Spiral. We see it very often in nature without realising it. However, it has not just been used in nature as it's allure and importance has long been recognised. Human folk have used it for design, architecture, music, logos, timing and so many other things. It's application is limited only by imagining ways it can be implemented. Here we are going to look at how it is created using the Fibonacci Sequence and why it is such a fundamental aspect of life.

Mike fashions the latest in spiral technology

Drawing the Golden Spiral

Open up your CAD package, click "File" and "New", just messing with ya, we'll do this on paper ;) You'll need the following:

• a blank sheep of paper
• a compass, the one that draws circles, the other type is not really useful to use now, same goes for a sat nav
• a straight edge (ruler)
• a pencil

These are the four things needed to start creating the universe ;)

On the blank sheep of paper be sure to leave enough space for drawing the whole process so take a look through the steps below to see how much space will be used because if you start using too much space at the beginning then you may run out.

1: Draw a Line

To get things started draw a line on the page. Locate it a bit left to the centre of the page.

2: Bisect the Line

We need to find the centre point of this line as it's going to play a large role in creating the golden spiral and rectangle. Place the point of the compass on one end of the line (on the yellow dot) and expend it out so that it goes out past the centre point of the line, judge this by eye. It can be as far past the centre point as you like but you might run out of space on your paper!

Draw a small arc as indicated below. The idea is that this arc will pass over the actual centre point of the line. Do this above and below the line as shown.

Do the exact same process on the other end of the line, i.e. place the point of the compass on the other end of the line. Make sure you don't extend out the compass any more, keep it as you had it for the last step.

All that's left to do now is to draw a line between the points where the arcs meet. This line will exactly mark the centre point of the line, so be sure to mark it.

3: Draw a Circle

Place the point of the compass at the centre point of the line and extend it out to either end of the line. Now rotate the compass around to draw the circle.

4: Draw Another Circle

Keeping the compass at the same width place the point of it at the right end of the line. Draw another circle here. This circle will be the exact same size as the last circle.

5: Draw a Central Vertical Line

From where the circles meet at the top draw a line down to our original line.

6: Draw a Small Circle

Place the point of the compass where the two lines meet and extend it out to the right end of the original line. Now draw the little circle!

6: Draw a Reference Line

This next line is going to help us locate the top left corner of the golden rectangle. Using your straight edge draw a line from the right end of the original line ensuring that it passes through where the second line and small circle meet. Carry drawing the line a good distance out beyond the left circle.

7: Arc Crossing Reference Line

Place your compass point at the left end of the original line and extend it out to the full distance of the original line. Then draw and arc so that it crosses through our reference line we drew in the last step.

8: Second Golden Rectangle Line

From where the arc and the reference line meet draw a line down to meet with the left end of the original line.

9: Complete the Square

Place the point of the compass at the top of the new line and stretch the compass out to the bottom of the line. Now draw an arc to the right as below.

Keeping the compass at the same width place the point at the right end of the original line and draw an arc so that it crosses through the arc we just drew. This gives us the top right corner of our square.

10: Complete the Square

Connect up the points.

Now we have the square part of the golden rectangle.

11: Remove Unnecessary Lines

Now that we have our square you can erase all the extra lines that we used to get to this point except for the line we used to mark the middle of the original line.

12: Marking the Bottom Right

To find the bottom right of the golden rectangle place the point of the compass on the middle of the original line and extend the compass to the top right corner of the square. Then draw an arc to the right of the original line.

13: Completing the Bottom of the Golden Rectangle

Now just extend the original line out to meet the arc!

14: Marking the Top Right

Repeat what we did in step 12 except with the top of the square. You already know how to find the centre of a line, you'll need that too.

15: Completing the Golden Rectangle

Now complete the golden the rectangle by drawing a vertical line from the top right to the bottom right. Carrying right on place the compass point on the top right corner and extend it out to the left to meet the top of the vertical line. Draw an arc that crosses the right line of the rectangle.

16: Close the Square

From where the arc meets the line draw a horizontal line to the left until it meets the vertical line to the left.

17: Create the Remaining Squares

Just repeat the above process as many times as you like. I've got you started with indicating where to place your compass point in order to indicate where to draw the lines to make the squares.

That leaves us with the Golden Rectangle with more golden rectangles contained within it!

18: Starting the Golden Spiral

Place the point of the compass at the bottom right of the main square and draw an arc as indicated.

Repeat using the point indicated as to where to position your compass.

To finish off the spiral simply follow the image below for a guide as to where to place your compass to draw the next arc.

19: Woohoo! You Did It!

Well done! Here's how it looks without the squares and rectangles.

The Big Deal

Now that you know how it works and are familiar with drawing it you can take a measuring tool to each of the squares and rectanges you have drawn. What's you'll notice is that the length of the lines have a Fibonacci relationship to each other!

Next we take a look at a few places where nature uses the spiral.