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 door The Golden ratio, also known as The foretell Proportion, The Golden Mean, or Phi, is a constant that fanny be seen in all through show up the numerical world. This ir dimensionnal bit, Phi (? ) is bear upon to 1. 618 when rounded. It is described as dividing a bed in the extreme and mean ratio. This means that when you divide segments of a line that always have a same quotient. When lines like these atomic number 18 separate up, Phi is the quotient When the opprobrious line is 1. 18 (Phi) times larger than the no-count line and the gruesome line is 1. 618 times larger than the red line, you argon able to go back Phi. What makes Phi such a mathematical phenomenon is how often it weed be open up in many divergent places and situations all over the world. It is seen in architecture, nature, Fibonacci numbers, and still more amazingly,the human body. Fibonacci Numbers have proven to be nearly related to the Golden Ratio. They be a series of numbers fuck off by Leonardo Fibonacci in 1175AD. In the Fibonacci series, every number is the tot up of the two before it.The barrier number is known as n. The first full term is Un so, in order to find the next term in the sequence, the last two Un and Un+1 are added. (Knott). Formula Un + Un+1 = Un+2 Example The second term (U2) is 1 the third term (U3) is 2. The fourth term is going to be 1+2, making U3 equal 3. Fibonacci Series 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 When each term in the Fibonacci Series is divided by the term before it, the quotient is Phi, with the exception of the first 9 terms, which are still very dummy up to equaling Phi. Term (n) First Term Un SecondTerm Un+1 Second Term/First Term (Un+1 /Un) 1 0 1 n/a 2 1 1 1 3 1 2 2 4 2 3 1. 5 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 Line s that follow the Fibonacci Series are rig all over the world and are lines that can be divided to find Phi. One interesting place they are found is in the human body. Many examples of Phi can be seen in the hands, face and body. For example, when the length of a some mavens forearm is divided by the length of that persons hand, the quotient is Phi.The distance from a persons operate to their hitchhiketips divided by the distance from that persons head to their elbows equals Phi. (Jovanovic). Because Phi is found in so many natural places, it is called the Divine ratio. It can be tested in a number of ways, and has been by various scientists and mathematicians. I have chosen to investigate the Phi constant and its bearing in the human body, to find the ratio in different surface lot and see if my results match what is pass judgment. The aim of this probe is to find examples of the number 1. 618 in different people and investigate other places where Phi is found.Three ratios will be compared. The ratios investigated are the ratio of head to toe and head to sensetips, the ratio of the last-place branch of the proponent figure to the pump section of the index fingers breadth, and the ratio of forearm to hand. FIGURE 1 FIGURE 2 FIGURE 3 The first ratio is the white line in the to the light blue line in FIGURE 1 The second ratio is the ratio of the black line to the blue line in FIGURE 2 The third ratio is the ratio of the light blue line to the sulky blue line in FIGURE 3 METHOD practice Specific body parts of people of different ages and genders were measured in centimeters.Five people were measured and each participant had these parts measured * space from head to foot * Distance from head to fingertips * Length of lowest section of index finger * Length of middle section of index finger * Distance from elbow to fingertips * Distance from wrist to fingertips The ratios were found, to see how closing curtain their quotients are to Phi (1. 618). Then the percentage battle was found for each result. PARTICIPANTS The people were of different ages and genders. For variety, a 4- course-old fe manlike person, 8-year-old mannish, 18-year-old egg-producing(prenominal), 18-year-old male and a 45-year-old male were measured.All of the measurements are in this investigation with the ratios found and how close they are to the constant Phi are analyzed. The results were put into tables by each set of measurements and the ratios were found. DATA Participant meter ( 0. 5 cm) Measurement 4/female 8/male 18/female 18/male 45/male Distance from head to foot 105. 5 124. 5 167 one hundred eighty 185 Distance from head to fingertips 72. 5 84 97 110 115 Length of lowest section of index finger 2 3 3 3 3 Length of middle section of index finger 1. 2 2 2. 5 2 2 Distance from elbow to fingertips 27 30 40 48 50Distance from wrist to fingertips 15 18. 5 25 28 31 RATIO 1 RATIO OF school principal TO TOE AND HEAD TO FINGERTIPS Measurements Parti cipant 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 original quotients that were found from the measurements. According to the Golden Ratio, the expected quotients will all equal Phi (1. 618). Distance from head to footDistance from head to fingertips 1. 4-year-old female 105. 0. 5 cm/ 72. 50. 5 cm = 1. 455 1. 2% 2. 8-year-old male 124. 50. 5 cm/ 850. 5 cm = 1. 465 1. 0% 3. 18-year-old female 1670. 5 cm/ 970. 5 cm = 1. 722 5. 2% 4. 18-year-old male 1800. 5 cm/ 1100. 5 cm = 1. 636 1. 0% 5. 45-year-old male 1850. 5 cm/ 1150. 5 cm = 1. 609 0. 7% How close each result is to Phi This shows the exit amid the actual quotient, what was measured, and the expected quotient (1. 618). This is found by subtracting the actual quotient from Phi and using the absolute value to get the difference so it does not give a negative answer. 1. 18-Actual Quotient=difference in the midst of result and Phi The difference between each quotient 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 find how close the results are to the expected value of Phi, percentage error can be used. Percentage error is how close experimental results are to expected results.Percentage error is found by dividing the difference between each quotient and Phi by Phi (1. 618) and multiplying that result by deoxycytidine monophosphate. This gives you the difference of the actual quotient to the expected quotient, Phi, in a percentage. (Roberts) Difference1. 618 x100=Percentage difference between 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. 1 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% depth psychology The highest percentage error, the percent difference between the result and Phi, is 10. 1 0. 12%. This is a small percentage error, and means that all but one of the ratios was more than 90% accurate. This is a good example of the Golden Ratio in the human body because all the values are close to Phi. Also, as the age of the participants increases, the percentage error decreases, so as people get older, the ratio of their head to feet to the ratio of their head to fingertips gets closer to PhiRATIO 2 RATIO OF THE MIDDLE partition OF THE INDEX FINGER TO THE BOTTOM SECTION OF THE INDEX FINGER Measurements Participant Length of lowest section of index finge r (0. 5 cm) Length of middle section of index finger (0. 5 cm) 4 year old female 2 1 8 year old male 3 2 18 year old female 3 2. 5 18 year male 3 2 35 year old male 3 2 Ratios Length of lowest section of index finger Length of middle section of index finger 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 result is to Phi 1. 618-Actual Quotient=difference between result and Phi The difference between each quotient 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 difference between 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. 617. 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 ratio, 3 of the results come out with a