Fibonacci Sequence in Nature

Fibonacci lukujono luonnossa

1 - 1 - 2 - 3 - 5 - 8 - 13 - 21 - 34 - 55 - 89 - 144 ....

The Fibonacci sequence is mathematical, in which each number is the sum of the two preceding ones. The sequence often appears in nature, such as in the arrangement of leaves and phenomena related to plant growth. The arrangement of leaves in many plants, the placement of seeds in sunflowers, and the scales of pinecones follow the Fibonacci sequence. This helps plants optimize their intake of light and nutrients.

For example, rabbits reproduce according to the Fibonacci sequence, under the assumption that each pair produces a new pair in every subsequent month. The Golden Ratio is also often used in art and architecture, and it is closely related to the Fibonacci sequence. The Golden Ratio, with the value 1.618, can be found by dividing successive Fibonacci numbers.

In painting and sculpture, the Fibonacci sequence and the Golden Ratio are used to create aesthetically pleasing and harmonious compositions. The Fibonacci sequence is applied in various algorithms and data structures, such as recursive programming and sorting algorithms. Fibonacci numbers appear in many problems of combinatorics and numerical analysis. The Fibonacci sequence and the Golden Ratio are also used in market analysis and in forecasting economic cycles. Analysts employ Fibonacci retracement levels in the analysis of stock prices. In some musical compositions, the Fibonacci sequence and the Golden Ratio have been used to construct rhythms and melodies. Nor should we forget the structuring of film scenes in relation to the Golden Ratio.

Compiled by Domestic Sales Personnel

Proportional Limity

0 (0)   Initially, there is no idea of activity.

1 (1)   A gets the idea of domestic sales.

1 (2)   A's first month of activity. The new representative studies for a month.

2 (3)   (A + B) Each one finds a sub-representative after a month.

3 (4)   (A - C) + B studies for a month.

5 (5)   (A + D) + (B + E) + C studies for a month.

8 (6)   (A + F) + (B + G) + (C + H) + D studies for a month. Instead of eight, there are seven representatives.

There is a proportional limity in phenomena, after which things do not follow the pattern of Pascal's triangle and, in this case, the Fibonacci sequence. The sixth time is excessive in many considerations, and this corresponds to the number of our fingers. Which finger are you willing to remove, or how many more fingers do we want on our hand?

Fibonacci Sequence in Pascal´s Triangle

Proportional Limity in Pascal´s Triangle

1                            1                               1

2                       1        1                          1 x 11 = 11

3                    1      2      1                       11 x 11 = 121

4                1      3      3      1                    11 x 121 = 1331

5            1      4      6      4      1                11 x 1331 = 14641

6        1      5     10     10      5      1          11 x 14641 = 1      5     10     10      5      1

Pascal's triangle and the Fibonacci sequence form the limit of relativity after the fifth stage (also the proportional step). In practice, this means that the phenomenon changes as we observe it. This stage is bypassed by the concept of time dilation. First, we will consider the nature of the first two phenomena.

1 + 1 = 2

a + a = 2a

Measuring tape A is 100 cm long, and measuring tape B is 200 cm long. If we consider this as a phenomenon, in some cases, certain factors must be taken into account. In this case, the total length of measuring tape A is not 100 cm but likely 100 + 5 cm. Similarly, the length of measuring tape B is 200 + 10 cm due to the larger roll.

We need to consider the scale of the phenomenon. The casing of a 100 cm measuring tape is very likely 5 cm. Measuring tapes are designed so that, for example, the width of an opening can be measured by placing the tape into the opening. For measuring tape A, a reading of, say, 75 cm plus the 5 cm roll gives 80 cm. For measuring tape B, a reading of 70 cm, taking the roll into account, also results in 80 cm. In phenomena, it is essential to understand the simple rules, which vary depending on the context of observation.

A 100-meter running track's starting blocks

The 100-meter running distance begins with a starting block comparable to the casing of a measuring tape, described here as being 50 cm in length. The starting block has a significant impact on the resulting time, and the total length of the event, when described as a phenomenon, is not 100 m but 100 m + 0.5 m = 100.5 m.

These starting blocks are designed to give sprinters a powerful and stable launch. These blocks are adjustable, allowing athletes to set the angle and position that best suit their starting stance and technique. They play a crucial role in maximizing the sprinter's initial acceleration and overall performance.

The world record times for the 100 and 200 meters are as follows:

• 100 meters: 9.58 seconds, set by Usain Bolt (Jamaica) on August 16, 2009, in Berlin.

• 200 meters: 19.19 seconds, also set by Usain Bolt on August 20, 2009, in Berlin.

1 - 1 - 2

9.58 - 9.58 - 19.16

The golden ratio, often represented by the Greek letter φ (phi), is a special mathematical constant approximately equal to 1.6180339887.... It's derived when a line is divided into two parts such that the ratio of the whole line to the longer part is equal to the ratio of the longer part to the shorter part.

4.60 / 8.80 m = 0.523 m ( Ancient Egyptian Royal Cubit)

Basic profile for ratio calculation HEB 100 for strength calculation

    450 / 90 = 5

Staatic Values HEB 100 y - y              I = 167 cm⁴
                                                            W = 33.5 cm³

 167 / 33.5 = 5

Length of basic profile for EP Calculation 523 mm

The calculated profile length is 520 cm, when the profile is 523 cm long. The profile must extend 1.5 cm beyond its support points on each side so that the profile remains bent and supported by its support points. 520 cm + 2 x 1.5 cm = 523 cm (523 mm = Ancient Egyptian Royal cubit.)

F = 1 kN     Ix = 450 cm⁴    L = 520 cm  E = 20 600 kN/cm²

Kokonaistaipuma muodostuu pistekuormasta: 0,316 cm (käytännössä pii = 3,14 = π)
Kannattimen omasta painosta 1,042 kN: 0,2057 cm

Literature uses a modulus of elasticity value of 21,000 kN/cm², but in my calculation, I have used a value of 20,600 kN/cm². This results in a higher deflection value, but it remains on the safer side for various calculations. In ancient times, such deflection values were determined based on known principles, making the computation straightforward. Nowadays, with just a few keystrokes and, in some cases, logical reasoning, the calculations are performed effortlessly.

Kaksitukinen kannattaja, jossa tasainen kuorma 1,042 kN - HEB 100 - L520 cm

Double-support beam with uniform load 1.042 kN - HEB 100 - L520 cm

Physiology is in many senses, a deflectiona

In the SI system, we measure a meter with the unit of 100 cm. In ancient times, the concept of the smallest unit was known. In physiology, this refers to the 100-meter running distance, which is the shortest unit, as no one runs that distance while accelerating their speed. Acceleration occurs, depending on the athlete, over a distance of 50-70 meters. In practice, the average time for all competitive runners is around 10 seconds. For example, in our country, no one has run a time of 10 seconds. Nowadays, running is further aided in many ways, from running surfaces to shoes, and minor doping cannot be ruled out. In nature, there is no doping or artificial assistance.

• 100-meter Sprint:

  • Length = 100 m

  • Approximate time = 10 s

  • Average running speed = 10 m/s (36 km/h)

• Decimation & Physics Constants:

  • Decimal system relies on the base "10"

  • Gravitational acceleration: 9.82 m/s²

  • 1 kilonewton (kN) = 102 kg (approximately the weight supported by 1 kN under Earth's gravity)

• Relativity (Time Dilation):

  • At 0.25c (where c = speed of light), time dilation factor = 1.0328

  • Division results:

    • 102 kg ÷ 9.82 m/s² ≈ 10.38 (force in kilonewtons)

    • 10.38 ÷ 10 = 1.038

• Usain Bolt:

  • Weight: 94 kg

  • Time: 9.58 seconds for 100 m sprint

  • Scaling calculation: 9.58 ÷ 9.4 = ~1.02

Let's play with the following idea, or is it a game?

Let's imagine the HEB100 profile in the picture to be 200 cm long. In order for the profile to remain bent on the supports, the span should be 197 cm.

100 meters: 9.58 seconds, set by Usain Bolt (Jamaica) on August 16, 2009, in Berlin.

200 meters: 19.19 seconds, also set by Usain Bolt on August 20, 2009, in Berlin.

Next, we calculate the deflections of the support without formulas

4.11.2015*22:50 (913 - 397)
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