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)

Answer 1

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 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.

• 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).

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

Answer 2

I understand your question to be, how do you create a logo with the golden ratio? I feel as if your question is more theoretical than program based? Here is my theoretical answer and I will be the Devil's Advocate for the golden ratio here (as I believe many of the comments above don't completely understand the significance).

Sketch on paper. That's how the best logo's start. Do NOT try to create the above schematic and fit a logo into it. As other's have said, these images you have above are more for marketing than they are how the designer actually created them.

After you have your base idea (IE: using the Twitter logo, let's say you know you want your logo to be a bird and you've sketched the basic shape of the Twitter logo) you can bring the sketch into Illustrator and begin doing the math. (IE: making sure it fits the golden ratio).

You do not need to create this type of "grid" as you see in these photos and than fit the logo into it. Instead, you need to understand what the golden ratio is and how it can assist you. When you know how you want it to assist you, you can start doing the math.

We'll use Twitter as an example. What we're looking at in this one is the size of the circles (that is what is important). This "golden rectangle" you're seeing everywhere is actually the Fibonacci Sequence of numbers (you'll also see it with a spiral, which is what many artists use to create a directional eye flow in their pieces). So you see the "main", large circle here is the size of the bird's body. Or, at least, the bottom of the bird's body is following the curve of this circle. This is the main diameter (width) we'll be utilizing to use the golden ratio to get the size of the bird's wings, feathers and head based off of the size of his body.

To SHOW you the relationship between the objects the designers have placed the Twitter bird into that golden rectangle we talked about. I, too, have a shape file in Photoshop and Illustrator to help measure with the golden ratio. HOWEVER, what they more likely did, was took the circumference of the bird's body and divided it by 1.6. 1.6 is the rounded golden ratio number. But visually, what this actually does, is makes the second smallest circle that you see the correct size in relation to the first, larger circle.

"Why does this matter? Why not just make a smaller circle and call it a day?" The answer is because everything comes down to the way our brains perceive the world around us. Naturally beautiful things--many things found in nature--have a size or spatial relationship utilizing this ratio. This means, our brains are more likely going to subconsciously recognize these relationships as beautiful. I have not yet had an instance where I utilized this relationship correctly prove that statement or philosophy ineffective. As a secondary benefit, if