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How to use Fibonacci numbers / Golden Ratio in logo design in Illustrator or Sketch?


Question

I am trying to get into Fibonacci/Golden Ratio logos for some university work however I'm fairly new to Illustrator. I've used Photoshop for about 8 years and Sketch v3 since it was released. However, I can't work out how people create these logos.

I'm trying to work out how for example you can go from a hexagon with pointed edges to using circles to pull the points into rounded edges.

Any help/tips or links to tutorials would be greatly appreciated.

Thanks

EDIT

Here are some examples (thanks Bakabaka for asking)

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2014/07/17
1
10
7/17/2014 9:58:00 AM

Your question looks theoretical but when reading more closely it sounds like you are asking how to merge shapes in Illustrator. There are multiple ways to make an hexagon with rounded points. Here is one that gives clean results but depending on the value you pick, might not look perfectly rounded :

  • Draw an hexagon using the polygon tool. You can click on the canvas with the mouse to enter exact measures.
  • Select the hexagon and go into the top menu bar Effects > Special > Rounded Corners
  • Activate the preview to see what you are doing and find a value that looks good. This is the radius so if you want to workout golden ration proportions with the exact measures of your hexagon you could do that there.

However, if you want to do it by hand a bit like the shots you've included in your question, here is how I would do it:

  • Draw an hexagon using the polygon tool. You can click on the canvas with the mouse to enter exact measures.

Draw an hexagon

  • Draw a circle using the proportion you want (then again, you can click directly on the canvas to enter an exact value).
  • Duplicate your circle at each point of the hexagon and place it extremely precisely (you will want to use the outline preview in Illustrator (ctrl+y). This step is extremely important, the circle needs to touch but shouldn't overlap. It might require a few attempts.

Put a circle in each point

  • Select your hexagon and all your circles at once.
  • With the Shape builder tool (Shift+M), hit Alt to obtain a minus sign on your cursor. Click on the canvas and drag to each hexagon points to remove them. (If the point doesn't show as a separate area, it's because your shapes are not touching properly).

Shape builder tool

  • Let go of Alt and click and drag your other shapes together to unite them.

Finished shape

2014/07/17
4
7/17/2014 2:32:00 PM