1. The Golden Ratio By :Marissa Murphy

2. What is The Golden Ratio? The Golden ratio which is represented by the Greek letter phi is a special number approximately equal to 1.618. The golden ratio appears in geometry, art, architecture, and in nature etc. The Golden ratio is said to be pleasing to the eye. To understand what the golden ratio is you have to understand the Fibonacci sequence. The Fibonacci sequence is the sequence of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144….The Fibonacci sequence is found by adding up the two numbers before it starting with 0,1 0+1=1and then 0+1+1=2 and then 2+1= 3 and then 2+3= 5 are you seeing the pattern? Hopefully you now understand the Fibonacci sequence, if you do then it will be easier for you to understand how the Golden Ratio comes from the Fibonacci sequence. If you take the ratio of any two of the sequential numbers from the sequence you will see that the larger the numbers the closer it gets to 1.618(phi)

3. Understanding What The Golden Ratio Stems From Hopefully you now understand the Fibonacci sequence, if you do then it will be easier for you to understand how the Golden Ratio comes from the Fibonacci sequence. If you take the ratio of any two of the sequential numbers from the sequence you will see that the larger the numbers get the closer it gets to 1.618(phi). Here is an example: 1/1=1 2/1=2 3/2=1.5 5/3=1.6666… 8/5=1.6 13/8=1.625 21/13=1.61538… 34/21=1.61904… Hopefully you now understand the Fibonacci sequence, if you do then it will be easier for you to understand how the Golden Ratio comes from the Fibonacci sequence. If you take the ratio of any two of the sequential numbers from the sequence you will see that the larger the numbers get the closer it gets to 1.618(phi). Here is an example: 1/1=1 2/1=2 3/2=1.5 5/3=1.6666… 8/5=1.6 13/8=1.625 21/13=1.61538… 34/21=1.61904…

4. What is Phi? The Golden ratio is one of the most irrational numbers and can be defined in terms as itself like this: (in numbers:1.618…=1+1/1.618…) This also can be expanded in fraction form which goes on forever and ever

5. The Golden Section For two quantities to have the golden ratio the sum of the two quantities and the larger one has to be the same as the ratio between the larger one and the smaller one. The ratio of the whole line (A) to the large segment (B) Is the same as The ratio of segment (B) to the small segment (C)

6. Where Can You Find The Golden Section/Golden Proportion? You don’t have to look far to find the golden section; just look down at your hand or in a mirror. The golden section can be found in your face and body. Many trainers use the golden ratio as a template for what their clients should strive for. Also plastic surgeons use it while doing plastic surgery. One surgeon actually made a template of the golden ratio to help to make sure everything is proportioned correctly.

7. Does Your Face Fit The Golden Ratio? Here is one way you can find out if your face fits the golden ratio:Here is one way you can find out if your face fits the golden ratio: 1. You have to take or find a picture of your face facing forward without an expression. 2. Next you need to download the template for the perfect golden ratio face(there is a female and male template) 3. Lastly you need to place the template over your picture, the closer it is to your face then the more proportioned and aesthetically pleasing to the eye it is.

8. Another Way To Find Out IF Your Face Fits The Golden Ratio… 1.You are going to have to measure the following things either in inches or centimeters but they all have to measured in the same measurement A= Top-of-head to chin=A= Top-of-head to chin= B= Top-of-head to pupil=B= Top-of-head to pupil= C= Pupil to nose-tip=C= Pupil to nose-tip= D= Pupil to lip=D= Pupil to lip= E= Width of nose=E= Width of nose= F= Outside distance between eyes=F= Outside distance between eyes= G= Width of head=G= Width of head= H= Hairline to pupil=H= Hairline to pupil= I= Nose-tip to chin=I= Nose-tip to chin= J= Lips to chin=J= Lips to chin= K= Length of lips=K= Length of lips= L= Nose-tip to lips=L= Nose-tip to lips=

9. 2. Next you need to divide the following measurements to find the ratio of your face, the closer the ratios are to 1.618 then the better proportioned your face is 2. Next you need to divide the following measurements to find the ratio of your face, the closer the ratios are to 1.618 then the better proportioned your face is A/G=B/D=I/J=I/C=E/L=F/H=K/E=

10. Finding The Golden Section/Proportion In Your Body 1. You are going to need the same as you needed to measure your face. You will need a measuring tape or stick, pencil and a piece of paper 2. Next you need to take these measurements2. Next you need to take these measurements A = Sole to belly button= B= Sole to top-of-head=B= Sole to top-of-head= C= Sole to knee=C= Sole to knee= D= Sole to navel=D= Sole to navel= E= Navel to shoulder=E= Navel to shoulder= F= Navel to top-of-head=F= Navel to top-of-head= G= Knees to calf muscle=G= Knees to calf muscle= H= Knees to sole=H= Knees to sole= I= Navel to mid-thigh=I= Navel to mid-thigh= J= Navel to knees=J= Navel to knees= K= Navel to sternum(mid-chest)=K= Navel to sternum(mid-chest)= L= Navel to base of the throat=L= Navel to base of the throat=

11. More measurements… M=Throat base to temple or brow bone=M=Throat base to temple or brow bone= N=Throat base to top-of-head=N=Throat base to top-of-head= O=The end of the calf muscle down to your ankle=O=The end of the calf muscle down to your ankle= P=Calf muscle to soleP=Calf muscle to sole Q=Mid-thigh to start of the kneecap=Q=Mid-thigh to start of the kneecap= R=Mid-thigh to end of kneecap=R=Mid-thigh to end of kneecap= S=Navel to crotch=S=Navel to crotch= T=Navel to mid-thigh=T=Navel to mid-thigh= U=Navel to sternum base=U=Navel to sternum base= V=Navel to sternum(mid chest)=V=Navel to sternum(mid chest)= W=Throat base to top-of-ear or brow bone=W=Throat base to top-of-ear or brow bone=

12. The Last Step… 3. Lastly you need to divide the following measurements. The closer the ratio of the two measurements are to 1.618 then the better the proportion and the more aesthetically pleasing your body is to the eye.proportion and the more aesthetically pleasing your body is to the eye.A/B=C/D=E/F=F/G=G/H=H/I=I/J=

13. The Last Bit Of Measurements! J/K=K/L=M/N=O/P=Q/R=S/T=U/V=W/X=