The Golden Spiral: How to Draw ItIntroductionThere'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 SpiralOpen 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 LineTo get things started draw a line on the page. Locate it a bit left to the centre of the page.

2: Bisect the LineWe 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 CirclePlace 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 CircleKeeping 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 LineFrom where the circles meet at the top draw a line down to our original line.

6: Draw a Small CirclePlace 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 LineThis 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 LinePlace 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 LineFrom 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 SquarePlace 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 SquareConnect up the points.

Now we have the square part of the golden rectangle.

11: Remove Unnecessary LinesNow 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 RightTo 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 RectangleNow just extend the original line out to meet the arc!

14: Marking the Top RightRepeat 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 RectangleNow 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 SquareFrom 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 SquaresJust 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 SpiralPlace 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 DealNow 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!

The Golden Ratio: segment, rectangle, spiral.

With these constructions, you now have a large vocabulary of Sacred forms to contemplate, draw, study and have fun with. Needless to say, what you can do creatively with these forms is unending. I encourage you to experiment and play with the constructions, wether it is making mandalas and abstract images, analizing and justifying nature objects, designing architectural features and objects or simply getting practice with your compass. Change a thing here and there, see what happens when you revert the order of steps, connect different forms, explore and experiment. You will be amazed to see how connected to each other these forms can be, and once you start making connections you will find that really, all these forms are VERY closely related, visually and metaphorically. Remember, we are always trying to see the multilayered nature of these forms, both in their immediate shape and in their deeper meanings and connotations. Here is an example of something I did, connecting the pentagon, the golden isosceles and the golden spiral. We will get into more advanced constructions and connections as we go.

I also wanted to briefly recall here a bit about what we discussed regarding Phyllotaxis. The whole of class 3 was devoted to the topic of geometry in nature. Hence, the form and features of the plant kingdom were greatly discussed. Phyllotaxis literally means "plant growth". We learned that the entire range of forms in the plant kingdom can be studied through the lense of phyllotaxis. We covered the four basic types of phyllotaxis: distichous, whorled, spiral and multijugate. We discovered that most plants feature spiral and whorled phyllotaxis. More importantly for our class, we learned that, in one particular study, out of the vast amount of plants that displayed spiral and whorled phyllotaxis it was found that 92% of them showed fibonacci phyllotaxis! This means that the Fibonacci sequence and our golden number PHI are very much a big part of the plant world. Briefly, the Fibonacci sequence involves numbers that are in a series where any number is the sum of the two preceding numbers. Therefore we have: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ... As we approach the fifteenth digit, dividing a number in the sequence by the previous number gives us a result which is closer and closer to PHI= 1.61803... As you learned in our Golden Ratio lesson, this is the "magic" number that is so crucial to the entire development and practice of Sacred Geometry. This is the reason why phyllotaxis (which is also in connection with the torus) is an important development to keep in mind. So next time you see a pinecone or a sunflower, go ahead and count the "parastichies" or spirals, and you will find that they are two consecutive numbers in the Fibonacci sequence, almost ALWAYS.