golden spiral form, shown in Figure 19 (a) (c) and (d). Tibia Shellspiral growth is not like golden spiral but the sections of the spiral body can be described by the golden mean properties[1]. Golden spiral also be found on the tail of Sea Horses. The Star fish has the structure like a pentagram which has a close intimacy with golden ratio. The body sections of ants are to the Golden Ratio. The same properties also are found on the beautiful design of butterfly wings and shapes. The natural design of Peacock’s feather also goes to the golden ratio[17]. (a) (b) (c) Figure 20. Golden Section appears in (a) ant’s body parts, (b) peacock’s feather and (c) natural design of a butterfly The Golden Ratio is also found all throughout the physical universe. Weather patterns, Whirlpool have almost the same form like the golden spiral. Even the Sea Wave sometimes shows almost the same spiral pattern. The three rings of Saturn are designed naturally based on the Golden Ratio. The Galaxy, Milky Way, also has the spiral pattern almost like golden spiral. Relative planetary distances of Solar System also have the golden ratio properties. The orbital distances of planets are generally measured from the Earth. Mercury is the first planet of the solar system where the Earth is on third. So, to take the measurements from Earth would be like starting the Fibonacci numbers from somewhere in the middle of the sequence. If the measurement is started from the first planet of the solar system, Mercury, a very special and interesting property will be outspread. The asteroid belt is a part of the solar system and the largest asteroid is Ceres, which is one third of the total mass of all the asteroids. So, Ceres could be the logical orbit. If the average of the mean planet orbital distances of each successive planet is taken in a relation to the one before it, the value will be following the golden ratio number. Mean distance in million kilometres as per NASA, Mercury 57.91, Venus 108.21, Earth 149.60, Mars 227.92, Ceres 413.79, Jupiter 778.57, Saturn 1,433.53, Uranus 2,872.46, Neptune 4,495.06, and Pluto 5,869.66. Relative mean distances where Mercury is considered at the beginning, 1.00, 1.86859, 1.38250, 1.52353, 1.81552, 1.88154, 1.84123, 2.00377, 1.56488, and 1.30580 respectively. Total relative mean dis-tance is 16.18736 and the average is 1.61874 which is closer to the Golden ratio, 1.61803. (a) Galaxy (b) Galactic Pair (c) The rings of Saturn (d) Whirlpool (e) Weather pattern (f) Sea Wave (g) Planets of the solar system Figure 21. Some example of the physical universe where Golden Section properties are exists The Fibonacci sequence can be considered more or less the beauty of nature. The human body also exemplifies the mesmerizing occurrence of Golden Ratio. Total height of the body and the distance from head to the finger tips make the

12 Md. Akhtaruzzaman et al.: Geometrical Substantiation of Phi, the Golden Ratio and the Baroque of Nature, Architecture, Design and Engineering same ratio as Phi. Again the distances from head to naval and naval to hill also express the golden proportion[1,2,4]. The bones of fingers in human hand are related to each other by a ratio of Phi. For instance the proportion between the forearm

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- Summer '16
- Othina
- Test, Golden ratio, Golden Section, Golden Spiral