Mathematical beauty in life
Despite the constant transformations in the animal and human kingdom, symmetries and mathematical rules are also constantly observed. Just think about the symmetry in the bodies. Eyes, arms, legs, nostrils, ears, legs, everything is subject to the law of the mirror.
The following video is a good example for the relation between the beauty of the face and the golden ratio. Florence Colgate has been voted the britain "most beautiful face" for 2012. Watch this Phimatrix software analysis of her face.
The golden ratio present in facial symmetry has been studied in depth as part of cosmetic surgery. www.goldennumber.net
This doctor explain how he uses the golden ratio for his work
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The Marquard Beauty Mask
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Clear relation between the cross section of the DNA and the double pentagon
The word COSMOS meaning order and harmony wonderfully describe this geometric shape gathering Pi and Phi in the shape of life and in the COSMetic of the face. Optimisation in order to produce miniaturisation and beauty of the shape. The Pentagon based on Phi is the only polygon able to produce such a result. For more information about the geometry of this shape, follow this link.
Double pentagon and animal faces
If you want to draw the proportions of this Da Vinci model you should use the golden ratio
Leonardo commented: "Vitruvius wrote that human proportions are ordained by nature as follows:
* 4 fingers make a palm
* 4 palms a foot,
* 6 palms,a cubit,
* 4 cubits a double step and
* 24 palms a man's length."
Palm, cubit and foot, were used in the measurement system of the cathedral builders of the Middle Ages. It is based on the Fibonacci sequence.
* 4 fingers make a palm
* 4 palms a foot,
* 6 palms,a cubit,
* 4 cubits a double step and
* 24 palms a man's length."
Palm, cubit and foot, were used in the measurement system of the cathedral builders of the Middle Ages. It is based on the Fibonacci sequence.
In this measurement system, the smallest unit is the "line" ~ 2; 25 mm, diameter of a grain of barley.
palm = ~ 7.65 cm = 34 lines (34 = Fibonacci)
palm = ~ 12.4 cm = 55 lines (55 = Fibonacci)
the span = palm palm + = ~ 20 cm = 89 lines (= 89 Fibonacci)
foot span = + = palm ~ 32 cm = 144 lines (144 = Fibonacci)
cubit foot = ~ = span + 52.36 cm = 233 lines (233 = Fibonacci)
The complete cane palm + palm + = + foot span = 555 + angled lines
All this gives us a Vitruvian Man of almost 1,83 meter
palm = ~ 7.65 cm = 34 lines (34 = Fibonacci)
palm = ~ 12.4 cm = 55 lines (55 = Fibonacci)
the span = palm palm + = ~ 20 cm = 89 lines (= 89 Fibonacci)
foot span = + = palm ~ 32 cm = 144 lines (144 = Fibonacci)
cubit foot = ~ = span + 52.36 cm = 233 lines (233 = Fibonacci)
The complete cane palm + palm + = + foot span = 555 + angled lines
All this gives us a Vitruvian Man of almost 1,83 meter
The nautilus is not a fibonacci spiral, as we see so many times, however its proportions are still based on the golden ratio.