Turning area to aligns with scaleable vertical area in the golden ratio

Hi there,

I hope someone can help me out:

I am trying to draw a cube, of which the side panels are made up in the golden ratio. Problem is, it doesnt add up in the end, as you can hopefully see in the red cricles in the picture. So i want to turn the yellow marked area a little steeper, while the green marked should remain horizontally only moving to the right a nutch. The blue side panel to wich the green is to be aligned with is scaleable. But how can i turn the yellow area, with the green area atached to it and simultaneously scale the blue panel a little bigger so that in the end green and side area share the same corner? the black marked edges indicate that they can not be changed in length. The arrwos are trying to indicate what i just tried to explain.
I hope i could make myself clear. help would be hugely appreciated.

I’m not sure what you mean, but is it one off these methods?

Sorry but to me it doesn’t make much sense.
If the side panel is grouped you could scale it to snap to the intersection of two guides, one being horizontal, the other being the diagonal direction of the pannel.

Hi thanks for the quick response but unfortunatley it doenst help me, if you look at my picture, in the red circle you see what is not lining up right. And since i cant chance the length of of the surfaces which in your model are blue and yellow and in mine green and yellow i dont now what to do.

@Wo3Dan if i do that the side panel is to high, and if i cut it off it loses its golden ratio.

i dont now how to show my problem clearer:

the problem is the excess in red, but i canot change either lenght of the green lines, only the angle in pink and the size of the side panel, which has to remain in the golden ratio and can not be higher that the rest of the cube.

I hope this helps to clearify:

My problem is the excess in red. But I cannot change either of the green lines. Only the angle marked in pink and the side panels size, but the side panel has to stay in the golden ratio and can of course not be higher than the rest of the top panel.

maybe this clearifies it:

the problem is the excess marked in red.
but i can only change the side panel, while keeping its golden ratio and i can change the angle marked in pink. but the green lines have to keep their lengths.

Why are you making these adjustments to the profile on the extrusion? It would seem that all your adjustments have to do with refining (for want of a better word) a profile based on the Golden Mean. By extruding the shape before you have achieved the exact required dimensions (or proportions) in the profile, you needlessly complicate your own task.

As to getting the right combination of angle and offset for the inclined edge (the “yellow area”) in the profile, it’s not clear what the problem is. Please clarify.


you need to add the skp, because your image isn’t making sense…


Perhaps the pie tool would help, if I understand the problem.



As Gully suggested, start with a 2D layout first. If the base is 24" and the two edges that cannot change are 9" and 18", then create the golden rectangle:

Draw the 9" line along the top of the rectangle:

Set the circle segments to 480 and create an 18" radius circle from the end of the 9" line:

Draw a line from the end of the 9" line (or the center of the circle since they are the same) to the intersection point of the circle and the rectangle:

Note that the 18" line is shy by about 3/10,000th of an inch (close enough for most uses). Clean up the geometry:

And then extrude the result 24" to make a square bottom:

I used simple numbers I made up as an example since you haven’t provided any of your own. Change them as needed and the geometry should work out for you :slight_smile:


Drawing a cube and making in golden ration makes no sense to me because by definition they are two different things. The golden ration is not a rule nor design requirement. That ratio that has been establish over the years to make the aesthetics of items look pleasing so it is not absolute. It is common practice to design say chest of drawers with the drawers meeting it as the size changes from large height to much smaller at top while keeping the ration w x L of any drawer meeting the ratio. That is done by using a recursion formula. You could make the side look that way by some small added detail. You could make the project area of the slant x L of top may accomplishing what you want.
My question : Why do you have to be so precise??

Without dimensions it is just guessing what the out come would be. You can establish heights distributed as golden ratio as noted in the sketch. For a+ a/.618+a/.618^2+a/.618^3 = Height. A is top rec height, a/.618 is secod etc 1. as shown and distributed as such. per golden ratio.
The last section may not not be golden pending what the design dimensions are, but you have latitude to make a number of changes.

One would hope that precision would result from using a program like SketchUp. However, aesthetics is in the mind of the beholder and, as you point out, sometimes it just isn’t meant to be. Here’s an observation from professional woodworker Graham Blackburn:

Designing something with perfect proportions is rarely possible in the real world. Almost every piece of furniture or woodwork will need to accommodate constraints imposed by details of function, joinery, or economics. But even the attempt to approach perfection (which may be defined as measurements that correspond precisely to a system like the golden ratio) is virtually guaranteed to produce a better result than designing with no regard for any such paradigm. Even if you are close to perfect proportions, the eye is inclined to accommodate slight imperfections and fill in the gaps. Don’t think that everything has to fit the formula exactly. Last, remember that we often adjust things by eye to make a piece look lighter or better balanced, and we do so by using techniques that are part of the everyday woodworking vocabulary. They include the calculated use of grain direction to imply movement; highly figured grain to help the eye see curves where none exist; finished edges and corners that give the impression of thickness or thinness; the use of molding to adjust an apparent golden rectangle or solid; the use of tapered legs to give the appearance of more closely approximating an ideal proportion; and the mixing and matching of many other design paradigms.

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Do not think I agree with his assertion golden ratio is precise. It is not uncommon when setting say drawers in a chest the dimension are calculated using 1.618 since it has been based on ~5000 years of what makes things look good and dimension are change empirically to better fit ones judgment. I can always make precise drawing with wildly wrong numbers. Even Su since it uses floating point math and cannot represent all the real numbers precisely.

Big thanks to all of you, the hint to start in 2D eased it alot. But the real eye opener came from @jimhami42, drawing the circle made it a piece of cake. (after a night of trying to pull my thoughts out of my own cognitive dead end). Heres the result:

Now there is one (new) question left: how can I achieve, that the intersection of the of the vertical edge of the rectangle and the and the radius of of my circle divides the rectangle’s vertical edge in the golden ratio. Analogous to the midpoint of my circle, which divides the horizontal lines in the golden ratio. To illustrate this question i have drawn a couple of possible rectangles of which only the smallest one seems to meet these characteristic more or less, but how to get it accurate?

I tried scaling a rectangle, which i divided up by hand, but since i can not grab it where i need to i cant make it work.

I’m a bit confused by this discussion. Is the real problem how to draw the profile’s sides to the golden ratio by any means, or how to do so using SketchUp?

Some basic points that seem to be overlooked in the discussion about precision:

  • SketchUp approximates a circle as a polygon no matter how many sides you specify, so intersections generated by a SketchUp circle are not even certain to lie on the mathematical circle represented by the polygon.
  • The golden ratio is a irrational number that can’t be represented exactly on any computer, so any solution will always be an approximation.

Choose something close enough and get on with life!