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, also known as The Divine Proportion, The Golden Mean, or Phi, is a constant that can be seen all throughout the mathematical world. This irrational number, Phi (Φ) is equal to 1.618 when rounded. It is described as "dividing a line 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 are divided, Phi is the quotient:
When the black line is 1.618 (Phi) times larger than the blue line and the blue line is 1.618 times larger than the red line, you are able to find Phi. What makes Phi such a mathematical phenomenon is how often it can be found in many different places and situations all over the world. It is seen in architecture, nature, Fibonacci numbers, and even more amazingly,the human body. Fibonacci Numbers have proven to be closely related to the Golden Ratio. They are a series of numbers discovered by Leonardo Fibonacci in 1175AD. In the Fibonacci Series, every number is the sum of the two before it. The term number is known as ‘n’. The first 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 close to equaling Phi. Term (n) | First Term Un | Second Term 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 |
GABRIELLE NAHAS
IBDP MATH STUDIES
THURSDAY, FEBRUARY 23rd 2012
WORD COUNT: 2,839
INTRODUCTION:
The Golden Ratio, also known as The Divine Proportion, The Golden Mean, or Phi, is a constant that can be seen all throughout the mathematical world. This irrational number, Phi (Φ) is equal to 1.618 when rounded. It is described as "dividing a line 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 are divided, Phi is the quotient:
When the black line is 1.618 (Phi) times larger than the blue line and the blue line is 1.618 times larger than the red line, you are able to find Phi. What makes Phi such a mathematical phenomenon is how often it can be found in many different places and situations all over the world. It is seen in architecture, nature, Fibonacci numbers, and even more amazingly,the human body. Fibonacci Numbers have proven to be closely related to the Golden Ratio. They are a series of numbers discovered by Leonardo Fibonacci in 1175AD. In the Fibonacci Series, every number is the sum of the two before it. The term number is known as ‘n’. The first 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 close to equaling Phi. Term (n) | First Term Un | Second Term 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 |
References: Jovanovic, Radoslav. "The Golden Section and The Human Body." Rasko Jovanovic 's World of Mathematics. 2001. Web. 22 Feb. 2012. Knott, Dr.Ron. "Who Was Fibonacci?" Fibonacci Numbers and the Golden Section. Mathematics Department of the University of Surrey, UK, 11 Mar. 1998. Web. 22 Feb. 2012. "Phi for Neo-phi-tes." Overview of Phi, the Golden Ratio / Divine Proportion and Fibonacci Numbers. PhiPoint Solutions, LLC., 1997. Web. 22 Feb. 2012. PhiPoint Solutions, LLC. "The Human Body." Human Body and Phi, the Golden Ratio. 1997. Web. 25 Feb. 2012. <http://www.goldennumber.net/body.htm>. Roberts, Donna. "Error in Measurement." Oswego City School District Regents Exam Prep Center. Oswego City School District Regents Exam Prep Center, 1998. Web. 22 Feb. 2012. <http://regentsprep.org/Regents/math/ALGEBRA/AM3/LError.htm>.