### The Golden Ratio

### You cannot DENY beauty.

For aesthetic reasons, the European Nail Association has decided to pre-define the nail proportions using golden ratio properties. Two quantities have the golden ratio (in Latin: sectio aurea, proportio divina) if the longer part divided by the smaller part is also equal to the whole length divided by the longer part.

The recognition of the golden ratio has been evidenced since the time of ancient Greece in mathematical writing (Euclid of Alexandria). Sporadically adopted in the later Middle Ages (Campanus of Novara) and particularly used during the Renaissance period (Luca Pacioli, Johannes Kepler), it was also utilised in philosophical and theological contexts. Since the 19th century, it began to be adopted in aesthetic theories (Adolf Zeising) and was also practised in artistic architectural and craft-based circles as the ideal principle for defining the most aesthetically-pleasing proportions.

https://www.world-nail-championship.com/wnc/index.php/competition#sigProId60257bddf7

The ENA has implemented its preference for nails using the following measurements: line segment AB of length 1 is divided by point T, so that length f of the largest section TB is the mean calculation of the difference between length n of the smallest and the entire line segment. In other words, AB : TB = TB : TA. The resulting difference is called the golden section of length AB. The relationship between both sections - TB : TA is termed the golden ratio. The symbol for the golden ratio is symbolised by the Greek letter Phi (Φ, φ). φ= 1,618

The corresponding formula equates to:

#### f= n * φ

f = n * 1,618

The length of the entire nail can be determined using the formula:

#### l = n +(n * 1,618)

Example:

Length of the nail-bed (n) = 25 mm

Length of the free edge (f) = 25 mm * 1,618 = 40.45 mm ≈ rounded down to 40 mm

Length of the entire nail (l) = 25 mm + ( 25 mm * 1,618 ) = 65.45 mm ≈ 65 mm

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