Finally we can check the more evident relations of the construct with the golden circles' map, radii Φ0, Φ1, Φ2, Φ3 (formerly named c1, c2, c3, c4), once again extraordinary. I hope to be clear without filling the figure with a lot of letters (leaving un­changed those of the former study). angle of the limbs, new afterthought 2023 After having run through my new pi-day domain, to disclose a still buried π, then climbed some secrets of the golden spiral, up to recognize an even more unexpected meaning of the small golden triangle (the great one was already defined as such), I can't help but exalt with the best con­struc­tion ever, the absolute relation of the pentagon with the golden ra­tio, rep­re­sent­ing it at the purest source of its geometric formation. That's it, where the small triangle looks like a three sides synthesis of the golden rectangle, binding its two long sides by their arcs of circle, and pro­ject­ing the [remaining] base twice through its arcs, up to cross the triangle sides, to draw a line through, and intersect the same at the two last pen­ta­gon vertices; not necessary though, arc intersections are sufficient! Like a pair of out­stretched wings… A unequalled masterpiece of that ESSENTIAL GEOMETRY which i try to ap­ply in all my researches. So pure and efficacious is this figure, that I won't add letters, to leave the reader to ex­plore its expressive beauty. Just note that the + sign marks the exact center of the rectangle. The BEST solution ever of the Golden Pentagon