Thinking about the construction you have to be careful to let enough wood left for the weight it will have to carry. I heard people say that the bookshelf will be too weak and instable. In my case I had 56*17 mm^2 area for each of 20 joints. The last 4 joints have the maximum load to lead from the board to the plank. But as it is not perfect let´s say that just the half of it will really carry.
loadstress*safety-factor <= comprehessive strength
and in the simple case of uniaxial compression:
loadstress = weight*9.81 / supporting area
((4*57*17)/2)*(comprehessive strength) / 9.81 = maximum weight.
Even if you have a safety-factor of 5 and a strength of 40N/mm^2 you will get 1,5 tons. But as it is just an approximation, reality can do things else. A sharp edge could case a crack and also moisture is a weakening factor for wood.
what is beautifull?
You need some regularity in your construction. Use same lengths if possible and try to follow the rules of the golden cut. But don't stick on it too hard. In some cases there is a new length you cannot use anywhere else and it won't matter. There are also some factors like perspective and so on. So it will not be usefull to use fibonacci or the golden cut strictly in the shelf-depth.
The most important thing is the regularity and the direct partition!
Fibonacci and the Golden ratio
Maybe everyone heard about some rules that make things look well-ordered and somehow beautiful. This rule is known as the golden ratio. The Fibonacci sequence mathematics are interconnected with the golden ratio.
Fibonacci sequence: 1,1,2,3,5,8,13,21,34
golden ratio: phi = 1.618033...
The golden rule is (in our case) telling us something about the position of an seperator between two areas. So area1 and area2. With the golden ratio you can make the bigger area1 phi times bigger than area2. (area1=phi*area2) The areas together are (1+phi)*area2. So you get two measurements out of one given.
For example you need space for books (height=20cm) you can go into the fibonacci sequence and use 32.360cm or 30 cm for the second seperation. Now you would have about 50cm. Now you may recognize the fibonacci sequence 2,3,5.
I used the 2m planks, the first shelf starts at 70 cm. So we have 1,3 m with books. This factors I can just use once. And I used 50 and 30, 15 and 25 cm on every part.
When drawing the curve: Don't forget that the wood-pieces are used for the whole length. The curve needs two ends that are parallel to the wall to get a smooth wave.
Trick: if you have a long metal ruler you can hold it parallel on both ends and the right shape will show up.