geometry.in.nature
Did you know that the feathers of a peacock are stunning examples of Fibonacci Spirals?
The peacock is an incredibly beautiful bird, and its geometric analysis provides mathematical evidence of the order, harmony, and intrinsic beauty in nature.
The wonderful color of its feathers is one of its main charms, but the way its tail is distributed is an aspect that undoubtedly contributes to our admiration.
The iridescent "eyes" at the end of each feather are all positioned in proportional ratios, gradually decreasing in size, based on the pentagon progressions. If the quadrants of the circle, encompassing the tail are divided into ten equal parts each, and the Fibonacci Spiral is overlaid on the radiant lines to match each angle, the resulting arcs will intersect at these pentagon progression angles, and these intersection points will be the centers for the "eyes" of each feather.
The top image of slide 2 is merely to demonstrate the plan that reveals the law of feather distribution and the various "eyes," since in nature, the separated feathers fold into catenary curves instead of remaining in straight lines, as in the diagram.
The "eyes" on a peacock's tail are at the intersection points of logarithmic spirals. Interestingly, a peacock's plumage shares the phyllotaxis pattern linked to the Golden Spiral, which also exists in numerous flowers, as can be seen in the center of a daisy. In other words, the lines in the image that connect the "eyes" of the peacock's plumage are identical to the logarithmic spirals used to reconstruct the daisy's pattern.
When circles are inserted between the spiral lines, the peacock's pattern is transformed into the daisy's central pattern.
This is not magic: it's the patterned beauty of natural efficiency, which is the very nature of nature.
