Salvador Dali applied in his 1947–1949 painting "Leda Atomica" a concept that relates to the golden ratio or its conjugate. It is well known that Dali used mathematical formulas to elaborate his works (e.g. golden ratio, catastrophe theory, etc.), this said, we are not talking here about a layman.
On the bottom right of the preliminary sketch, he writes a mathematical formula, from which I have only this example with limited resolution:
It seems to relate the pentagon/pentagram with the circle envelope via the conjugate of golden ratio: $\frac{R}{2} \sqrt{n-2 \sqrt{5}}.$
I used a placeholder $n$, not being sure what exactly this might be, and suppose $R$ denotes the radius of the circle.
My question is, what exactly does this mathematical formula describe specific in relation to the geometry in the painting, or generally in geometric terms?
Please pay attention, that this question is purely mathematical, and please avoid any kind of interpretations in the context of art.
Image source with permission of the author: https://medium.com/@vaseghisam/the-grand-equation-of-imagination-salvador-dal%C3%ADs-mathematical-surrealoscope-9a51d478cc61
Your "n" should be 10, as is seen on page 17 of Matila Ghyka's 1946 book The Geometry of Art and Life
Ghyka's claim is that the side of a regular pentagon inscribed in a circle of radius $R$ has length $$p_r \text{ side of regular pentagon} = \frac R 2 \sqrt{10-2 \sqrt 5}.$$ This seems to be what the blurry image of Dali's writing says. The formula is equivalent to the one given at the end of the a section of the Wikipedia article on regular pentagons: $$t = R\sqrt{\frac{5-\sqrt 5}2} = 2R\sin \frac\pi 5.$$
(The Wikipedia article about the painting cites a paper describing Ghyka's influence on Dali. This paper led me to Ghyka's book.)