Commonly found in nature, the well-known golden spiral is a unique shape, but it can be well delineated using the elements of the Fibonacci sequence. It is very simple to draw, and can be very beautiful when done correctly.
Steps
Method 1 of 2: Complete
Step 1. Get everything you need
You will need to draw a system of squares that will eventually inscribe the spiral, acting as a guide for your drawing. Get the materials, making sure you have everything: the list of what you need can be found in the "Things you will need" section.
Step 2. Draw the squares using the Fibonacci sequence
It works by adding the two previous numbers: you get the next one starting from 0 and 1; so it goes on like this 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 etc. The length of the side of each square must be equal to the number in the Fibonacci sequence (the 0 is obviously not necessary for the drawing of any square), but the starting point can be called (0, 0), if we set it that way. You'll have a 1x1 square (use whatever unit you want, you just have to be constant), with a second 1x1 square drawn next to it, to the left of the first. At the bottom, place the 2x2 and to the right the 3x3. At the top, place the 5x5, and then to the left the 8x8. Under all these squares, place the 13x13, and so on, up to the largest square your paper can fit.
Step 3. Arrange the squares
Draw each of these squares counterclockwise. This will lead to a spiral when you draw the curve through the squares (as explained below).
Step 4. Use the compass
Place your compass, point and pencil, as shown in the figure, with the width set to one unit (side of the first square). Rotate it 90 ° counterclockwise.
Step 5. Adjust the compass
Set the compass so that it is now 2 units wide. Again, rotate it 90 degrees counterclockwise. Then 3, then 5, then 8; continue with this procedure until each square has the curve inside it.
Step 6. Go over the spiral with ink
When you're ready, go over your drawing in ink, precisely following the line drawn in pencil. If you are aiming for greater accuracy, you can use a curvilinear to help you.
Step 7. Erase the guidelines
With the spiral drawn in pen, use the eraser to erase the squares made in pencil.
Step 8. Done
Congratulations, you just drew a golden spiral!
Method 2 of 2: Rectangles
Step 1. Draw a square with perfectly equal sides
Using a ruler and protractor can help you.
Step 2. Find the midpoint
Find the midpoint of one of the sides.
Step 3. Align a compass with the opposite corner
Take a compass and find one of the corners on the opposite side from where you found the midpoint. With the needle in the midpoint, place the pencil on the opposite corner.
Step 4. Extend the line
Rotate the compass until the pencil is in line with the side on which you took the midpoint. This point will now be the angle for the golden ratio rectangle.
Step 5. Draw the new rectangle
Using a ruler, extend the square into a rectangle using the point you found as one of the corners. This new rectangle can be used as the basis for drawing the spiral.
Advice
- Using a curvilinear can greatly increase your accuracy, but it takes some practice to find the correct curve and get it to work.
- Use a thick pen. This gives you a bigger "loophole" with the curve of the pencil, so if you start to stray a little too far, you can notice and make the correction without it being too noticeable.
