Golden Ratio in the Human Body

THE GOLDEN RATIO IN THE HUMAN BODY GABRIELLE NAHAS IBDP MATH STUDIES THURSDAY, FEBRUARY 23rd 2012 WORD COUNT: 2,839 INTRODUCTION: The Golden Ratio, otherwise called The Divine Proportion, The Golden Mean, or Phi, is a steady that can be seen all through the scientific world. This nonsensical number, Phi (? ) is equivalent to 1. 618 when adjusted. It is portrayed as â€Å"dividing a line in the outrageous and mean ratio†. This implies when you separate sections of a line that consistently have an equivalent remainder. At the point when lines like these are isolated, Phi is the remainder: When the dark line is 1. 18 (Phi) times bigger than the blue line and the blue line is 1. multiple times bigger than the red line, you can discover Phi. What makes Phi such a numerical wonder is the means by which regularly it very well may be found in a wide range of spots and circumstances everywhere throughout the world. It is found in engineering, nature, Fibonacci numbers, and considerably more amazingly,the human body. Fibonacci Numbers have demonstrated to be firmly identified with the Golden Ratio. They are a progression of numbers found by Leonardo Fibonacci in 1175AD. In the Fibonacci Series, each number is the total of the two preceding it.The term number is known as ‘n’. The principal term is ‘Un’ along these lines, so as to locate the following term in the arrangement, the last two Un and Un+1 are included. (Knott). Recipe: Un + Un+1 = Un+2 Example: The subsequent term (U2) is 1; the third term (U3) is 2. The fourth term will be 1+2, making U3 equivalent 3. Fibonacci Series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144†¦ When each term in the Fibonacci Series is separated by the term before it, the remainder is Phi, except for the initial 9 terms, which are still exceptionally near approaching Phi. Term (n)| First Term Un| SecondTerm Un+1| Second Term/First Term (Un+1/Un)| 1| 0| 1| n/a| 2| 1| 3| 1| 2| 4| 2| 3| 1. 5| 3| 5| 1. 667 | 6| 5| 8| 1. 6| 7| 8| 13| 1. 625| 8| 13| 21| 1. 615| 9| 21| 34| 1. 619| 10| 34| 55| 1. 618| 11| 55| 89| 1. 618| 12| 89| 144| 1. 618| Lines that follow the Fibonacci Series are discovered everywhere throughout the world and are lines that can be isolated to discover Phi. One intriguing spot they are found is in the human body. Numerous instances of Phi can be found in the hands, face and body. For instance, when the length of a person’s lower arm is separated by the length of that person’s hand, the remainder is Phi.The good ways from a person’s head to their fingertips isolated by the good ways from that person’s head to their elbows approaches Phi. (Jovanovic). Since Phi is found in such a large number of common spots, it is known as the Divine proportion. It tends to be tried in various manners, and has been by different researchers and mathematicians. I have decided to research the Phi consistent and its appearance in the human body, to discover the p roportion in various measured individuals and check whether my outcomes coordinate what is normal. The point of this examination is to discover instances of the number 1. 618 in various individuals and explore different spots where Phi is found.Three proportions will be looked at. The proportions researched are the proportion of head to toe and head to fingertips, the proportion of the most reduced segment of the pointer to the center area of the forefinger, and the proportion of lower arm to hand. FIGURE 1 FIGURE 2 FIGURE 3 The main proportion is the white line in the to the light blue line in FIGURE 1 The subsequent proportion is the proportion of the dark line to the blue line in FIGURE 2 The third proportion is the proportion of the light blue line to the dim blue line in FIGURE 3 METHOD: DESIGN: Specific body portions of individuals of various ages and sexual orientations were estimated in centimeters.Five individuals were estimated and every member had these parts estimated: * Distance from head to foot * Distance from head to fingertips * Length of most reduced segment of pointer * Length of center segment of forefinger * Distance from elbow to fingertips * Distance from wrist to fingertips The proportions were found, to perceive how close their remainders are to Phi (1. 618). At that point the rate distinction was found for each outcome. Members: The individuals were of various ages and sexes. For assortment, a 4-year-old female, 8-year-old male, 18-year-old female, 18-year-old male and a 45-year-old male were measured.All of the estimations are in this examination with the proportions found and that they are so near the consistent Phi are broke down. The outcomes were placed into tables by each arrangement of estimations and the proportions were found. Information: | Participant Measurement ( ± 0. 5 cm)| Measurement| 4/female| 8/male| 18/female| 18/male| 45/male| Distance from head to foot| 105. 5| 124. 5| 167| 180| 185| Distance from head to finger tips| 72. 5| 84| 97| 110| 115| Length of most minimal area of list finger| 2| 3| Length of center segment of record finger| 1. 2| 2. 5| 2| Distance from elbow to fingertips| 27| 30| 40| 48| 50|Distance from wrist to fingertips| 15| 18. 5| 25| 28| 31| RATIO 1: RATIO OF HEAD TO TOE AND HEAD TO FINGERTIPS Measurements Participant| Distance from head to foot ( ±0. 5 cm)| Distance from head to fingertips ( ±0. 5 cm)| 4-year-old female| 105. 5| 72. 5| 8-year-old male| 124. 5| 85| 18-year-old female| 167| 97| 18-year-male| 180| 110| 45-year-old male| 185| 115| Ratios: These are the first remainders that were found from the estimations. As indicated by the Golden Ratio, the normal remainders will all rise to Phi (1. 618). Good ways from head to footDistance from head to fingertips 1. 4-year-old female: 105.  ±0. 5 cm/72. 5â ±0. 5 cm = 1. 455  ± 1. 2% 2. 8-year-old male: 124. 5â ±0. 5 cm/85â ±0. 5 cm = 1. 465  ± 1. 0% 3. 18-year-old female: 167â ±0. 5 cm/97â ±0. 5 cm = 1. 722  ± 5. 2% 4. 18-year-old male: 180â ±0. 5 cm/110â ±0. 5 cm = 1. 636  ± 1. 0% 5. 45-year-old male: 185â ±0. 5 cm/115â ±0. 5 cm = 1. 609  ± 0. 7% How close each outcome is to Phi: This shows the contrast between the genuine remainder, what was estimated, and the normal remainder (1. 618). This is found by taking away the genuine remainder from Phi and utilizing the total an incentive to get the distinction so it doesn't offer a negative response. |1. 18-Actual Quotient|=difference among result and Phi The contrast between every remainder and 1. 618: 1. 4-year-old female: |1. 618-1. 455  ± 1. 2%| = 0. 163  ± 1. 2% 2. 8-year-old male: |1. 618-1. 465  ± 1. 0%| = 0. 153  ± 1. 0% 3. 18-year-old female: |1. 618-1. 722  ± 5. 2%| = 0. 1  ± 5. 2% 4. 18-year-old male: |1. 618-1. 636  ± 1. 0%| = 0. 018 5. 45-year-old male: |1. 618-1. 609  ± 0. 7%| = 0. 009 Percentage Error: To discover how close the outcomes are to the normal estimation of Phi, rate mistake can be utiliz ed. Rate blunder is the means by which close test results are to expected results.Percentage mistake is found by isolating the contrast between every remainder and Phi by Phi (1. 618) and duplicating that outcome by 100. This gives you the distinction of the genuine remainder to the normal remainder, Phi, in a rate. (Roberts) Difference1. 618 x100=Percentage distinction among result and Phi 1. 4-year-old female: 0. 163  ± 1. 2%/1. 618 x 100 = 10. 1  ± 0. 12% 2. 8-year-old male: 0. 153  ± 1. 0%/1. 618 x 100 = 9. 46  ± 0. 09% 3. 18-year-old female: 0. 1â ± 5. 2%/1. 618 x 100 = 6. 18  ± 0. 3% 4. 18-year-old male: 0. 018/1. 618 x 100 = 1. 11% 5. 45-year-old male: 0. 009/1. 618 x 100 = 0. 5% AVERAGE: 10. 1  ± 0. 12% + 9. 46  ± 0. 09% + 6. 18  ± 0. 3% + 1. 11% + 0. 55%/5 = 5. 48  ± 0. 5% ANALYSIS: The most noteworthy rate blunder, the percent contrast between the outcome and Phi, is 10. 1  ± 0. 12%. This is a little rate blunder, and implies that everything except one of the proportions was over 90% precise. This is a genuine case of the Golden Ratio in the human body since all the qualities are near Phi. Likewise, as the age of the members builds, the rate blunder diminishes, so as individuals get more established, the proportion of their head to feet to the proportion of their head to fingertips draws nearer to PhiRATIO 2: RATIO OF THE MIDDLE SECTION OF THE INDEX FINGER TO THE BOTTOM SECTION OF THE INDEX FINGER Measurements Participant| Length of most minimal segment of pointer ( ±0. 5 cm)| Length of center area of pointer ( ±0. 5 cm)| multi year old female| 2| 1| multi year old male| 3| 2| multi year old female| 3| 2. 5| multi year male| 3| 2| multi year old male| 3| 2| Ratios: Length of most reduced area of forefinger Length of center segment of pointer 1. 4-year-old female: 2  ± 0. 5 cm/1  ± 0. 5 cm = 2  ± 75% 2. 8-year-old male: 3  ± 0. 5 cm/2  ± 0. 5 cm = 1. 5  ± 42% 3. 18-year-old female: 3  ± 0. 5 cm/2.  ± 0. 5 cm = 1. 2  ± 37% 4. 18-year-old male: 3  ± 0. 5 cm/2  ± 0. 5 cm = 1. 5  ± 42% 5. 45-year-old male: 3  ± 0. 5 cm/2  ± 0. 5 cm = 1. 5  ± 42% How close each outcome is to Phi: |1. 618-Actual Quotient|=difference among result and Phi The distinction between every remainder and 1. 618: 1. 4-year-old female: |1. 618-2  ± 75%| = 0. 382  ± 75% 2. 8-year-old male: |1. 618-1. 5  ± 42%| = 0. 118  ± 42% 3. 18-year-old female: |1. 618-1. 2  ± 37%| = 0. 418  ± 37% 4. 18-year-old male: |1. 618-1. 5  ± 42%| = 0. 118  ± 42% 5. 45-year-old male: |1. 618-1. 5  ± 42%| = 0. 118  ± 42% Percentage Error: Difference1. 18 x100=Percentage distinction among result and Phi 1. 4-year-old female: 0. 382  ± 75%/1. 618 x 100 = 23. 6  ± 17. 7% 2. 8-year-old male: 0. 118  ± 42%/1. 618 x 100 = 7. 3  ± 3. 1% 3. 18-year-old female: 0. 418  ± 37%/1. 618 x 100 = 25. 8  ± 9. 5% 4. 18-year-old male: 0. 118  ± 42%/1. 618 x 100 = 7. 3  ± 3. 1% 5. 45-year-old male: 0. 118  ± 42%/ 1. 618 x 100 = 7. 3  ± 3. 1% AVERAGE: 23. 6â ±17. 7% + 7. 3  ±3. 1% + 25. 8  ±9. 5% + 7. 3  ±3. 1% + 7. 3  ±3. 1%/5= 14. 3  ± 36. 5% ANALYSIS: With this proportion, 3 of the outcomes come out with a <10% rate blunder, which means they are near Phi (1. 618).In the estimations, 3 of the members had a similar proportion of 3:2. This outcome is very fascinating