​In a previous post it was pointed out that the digital roots of the Fibonacci sequence produce an infinite series of 24 repeating numbers. This post discusses how the 24 repeating numbers relate to the dimension of time. 

The Fibonacci 24 Repeating Pattern
​
​First, the 24-repeating pattern follows an approximate sinusoidal pattern (Figure 1). The 24 repeating digital roots of the F sequence are: 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9. Numbers 7, 8, 2, and 1 are the only numbers not fitting the sinusoidal pattern. 

Figure 1. Digital roots of the 24-repeating pattern

The Calendar and the Golden Ratio
​
​Second,  the modern calendar, which originated in Egypt, is based on four numbers: 12, 30, 60, and 360. There is a logical reason for the use of these numbers. The Egyptians made their calendar and time systems correspond with the dodecahedron and golden ratio. To the Egyptians the golden ratio and number 5 were very sacred. The Egyptians were aware of the 5 platonic solids and considered the dodecahedron with 12 faces, 30 edges, and 60 planar angles on its surface to be very important. Further, a dodecahedron’s faces are pentagons (5 sides).

Figure 3. Egyptian Pharaoh Mask (Tutankhamun)

The ancient Egyptians were aware that Solar system cycles reveal the same numerical parameters of the dodecahedron (i.e., the cycle lengths of Jupiter, Saturn, and Solar system are 12-years, 30-years, and 60-years). Thus, a profound mathematical relationship exists between the Solar system and dodecahedron. This explains why the Egyptians and Plato chose the dodecahedron as the geometric symbol of the Universe. ​

​The Egyptians were the first to adopt a solar calendar in 4,000 B.C. The solar year was 365 days and divided into 12 months consisting of 30 days. Although the twelve 30 day months equaled 360 days, five holidays were added at the end of the year, thus totaling 365 (365 = 12 x 30 + 5). 

The Egyptians also divided time into the Hour, Minute, and Second. The unit of hour was chosen so 1-day=24 (2 x 12) hours. Further, 1-hour = 60 minutes, and 1-minute=60 seconds.

In fact, the origin of the word hour comes from the Egyptian god Horus. Horus in Egyptian mythology is symbolic of the sun. The word Horizon also comes from Horus.

In summary, an intimate connection exists between time and the golden ratio. Firstly, in terms of the 24-repeating sinusoidal pattern, and secondly in terms of the roots of our modern calendar in the 12-sided dodecahedron. 

The number "108" has long been considered a sacred number. In Hindu/Buddhist beliefs, there are 108 virtues to cultivate and 108 defilements to avoid, which speaks to the value of balance. Hindu/Buddhist malas (rosary) also contain 108 beads. In Islam, the number 108 sometimes is used in place of the name of God. There are also 108 movements in tai chi. The frequency with which the number 108 appears across religious disciplines is too great to be dismissed as coincidence. 

108 and Growth
​
​It may be pointed out that the number 108 connects the Sun, Moon, and Earth: The average distance of the Sun and the Moon to Earth is 108 times their respective diameters. While this is an astonishing example of the number 108 in the natural world, an even more amazing example is in the constant growth of a nautilus shell.
​
A nautilus shell is found to illustrate the 1.08 progression, small to large, of the rooms or segments of its shell. In other words, as the sea creature grows, each chamber of its shell's growth is 1.08 times larger than the last chamber, creating a logarithmic spiral within the exterior of the shell.  

108 and The Number 5
​
​​The number 108 is related to the number 5. The clue is related to the angle of the Pentagon, being 108˚.​

​108 and The Fibonacci Sequence
​
​To fully understand the significance of the number 108, it is necessary to understand the numerical science of decimal parity. 

In many ancient cultures (e.g., Egypt and India) decimal parity was used as a way to understand the truth of numbers.

Decimal parity is a method for breaking numbers down into single digits. For example, the decimal parity equivalent of the number 361 is 3 + 6 + 1 = 10 and 1 + 0 = 1. So the decimal parity equivalent of 361 is 1.

The first 24 numbers of the Fibonacci Sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657.

When decimal parity is applied to the Fibonacci sequence it is found there is a repeating series of 24 digits being the following: (0), 1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1.

If we add these 24 digits up, we find the number 108.

0 + 1 + 1 + 2 + 3 + 5 + 8 + 4 + 3 + 7 + 1 + 8 + 9 + 8 + 8 + 7 + 6 + 4 + 1 + 5 + 6 + 2 + 8 + 1 = 108

Amazingly, the 1.08 constant growth rate the nautilus uses to build its spiral shell is the same pattern that repeats every 24 numbers in the Fibonacci sequence.