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Been checking out a bunch of tutorials and came across this golden ratio technique. My math side loves the idea but I'm curious how it works.

In this logo I'm putting together using Illustrator, I have sunshine rays coming over some hills, all enclosed in a half circle. I get how I can make the half circle and hills, but what about the rays?

All the golden ratio tutorials use only curved lines but the rays are straight. Would I just manually add straight lines and use the circles for the ends of the rays? Any help and advice would be much appreciated. Thanks

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    My personal recommendaton would be to concentrate on building a good logo and not on using some weird ratio. Yes the golden ratio can be found plenty of times in nature. But so does any ratio. Also there is plenty of art out there which heavily uses the golden ratio and doesn't look any better than traditional art. In fact theese paintings often don't look that good because theese painters sometimes forget that it takes a bit more than a single ratio öattern to produce a good artwork – BlueWizard May 30 '17 at 5:14
  • Got you. The whole golden ratio thing grabbed my attention because of my love for math but I understand what you're saying. I originally tried to build the logo using the method I see most people using but I ran into a slight problem. After I put together the half circle, I tried to use the pen tool to create the hills but when I clicked on the edge of the half circle to start the anchor point, it wouldn't set the point as the start of a line. Hope I'm making sense but if you have the time, would you mind helping me out? – Cuevas May 30 '17 at 5:33
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The Golden Ratio is 1:1.618 and has nothing to do with circles per-se. The circles in your sample show the limit of sequence

You could use the Golden Triangle to define the rays. Or just use the 'Golden Section Ruler':

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  • Thanks for the info, I've never heard of that golden section ruler but I'll definitely be looking into it – Cuevas May 30 '17 at 7:17
  • How is 1.618 used to build the golden section ruler? I can see the squares 45 degrees to the center point but from there I'm lost. I'd like to build this in illustrator but my google skills aren't finding anything – Cuevas May 30 '17 at 7:42
  • See answer from user287001 below (which is great). A more traditional way to draw this would be start with a perfect square, and use a locus to find the perfect rectangles. Google will even add a snippet: Search for Draw golden ratio – Bruno May 31 '17 at 2:30
  • Euclid & Co. didn't have the number 1,618 which is only an approximation. Euclid & Co. defined the golden section as an equation between line lengths and showed, how it could be constructed by drawing. The numeric representation was born much later. It coudn't exist before the numbers. – user287001 May 31 '17 at 9:56
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This is only an addition to already useful answers. You wanted a golden ratio grid in the comments. Its here:

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  1. Draw a rectangle H=10 millimeters, W=16,18 millimeters. Goto Object > Transform > Scale and make a 161,8 % sized copy. Press Ctrl+D a few times to make more

  2. Align the rectangles to right and bottom

  3. Add lines to make a grid. Be sure that you have smart quides ON and snapping only to points ON. Group all parts to keep them together.

  4. Make a copy, Object > Transform > Reflect > Vertical gives to you the right part. Move the parts side by side and scale to the wanted size.

Ready

ADDENDUM: You might get it a little easier and also vertically symmetric, if you do step 1, but after it divide the result vertically and horizontally (Magenta) at the middle. Then add lines (Blue), group and scale.

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  • Really really appreciate you taking the time, it's exactly what I'm looking for. Thanks for the breakdown. – Cuevas May 30 '17 at 9:37
  • Regarding the addendum, do I add the lines using the pen tool with smart guide or is there a better method? – Cuevas May 30 '17 at 15:45
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    @Cuevas use the line drawing tool. Holding Shiff you get horizontal and vertical lines easily. Actually one vertical and one horizontal line are enough. Drag holding Alt makes copies.. The rectangles are unnecessary after drawing the lines in full length. – user287001 May 30 '17 at 16:06

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