Running head: THE GOLDEN MEAN

Are All Ethnicities’ Facial Proportions Defined By Phi

Shery Malik

South Forsyth High School

Table of Contents

Title page ........................................................................................................................Page # 1

Table of Contents ............................................................................................................Page # 2

Introduction ....................................................................................................................Page # 3

Methodology ...................................................................................................................Page # 4

Results ............................................................................................................................ Page # 5

Conclusion ......................................................................................................................Page # 6

Appendix A .................................................................................................................... Page #

Appendix B .....................................................................................................................Page #

Appendix C ..................................................................................................................... Page #

Appendix D ..................................................................................................................... Page #

Appendix E .......................................................................................................................Page #

Bibliography ................................................................................................................. Page #

Acknowledgements ........................................................................................................ Page #

Phi, the golden number, which happens to be 1.6180339874989 . . . and so on, is used for many purposes: architecture, art, and even human beauty! In addition, it’s also identified for the golden section, ratio or mean. In similarity to pi, Phi, is the ratio of one line segment that results when a line is divided in a very unique way. For example, the ratio of a whole line (A) to the larger line segment (B) is in proportion to the large segment (B) to the little segment C. In that sense, A is proportioned to B as B is proportioned to C. ( Phi for Neo-phi-tes, 2006)

From the ancient pyramids of giza to the soaring CN Tower in Toronto, it has all been constructed with accordance to Phi. The Divine proportion has played a huge role for centuries in ancient and modern architecture across the world. The pyramids were designed and proportioned with phi all throughout the pyramid. In addition, the ancient Greeks knew of a rectangle whose sides are in the golden proportions ( 1: 1.618). The golden rectangle appeared in many Greek temples, including the Parthenon. Also, phi carries us all the way through the Notre Dame in Paris. At the time, Leandro Da Vinci was familiar with it as the divine proportion and used it in the design. ( The Human Face,n.d).

Believe it or not, phi can even set standards for human beauty! According to Yosh Jefferson(1996), “ ideal facial proportions are universal regardless of race, sex, and age, and are based on divine proportions . To that extent, if the width of the face from cheek to cheek is 10 inches, then the length of the face from the top of the head to the bottom of the chin should be 16.16 inches to be in ideal proportions, thus defining beauty. Dr. Stephen Marquardt discovered that beauty is not only related to phi, but can be defined by all races and genders, cultures and eras with the beauty mask that uses the pentagon and decagon as its foundation. Both geometric shapes incorporate phi in all their dimensions. Therefore, beauty is based entirely on how closely one’s features reflect phi in their proportions. (Roger Herz 1998)

This experiment will examine whether the divine ratio, applies to different ethnic groups. By taking numerous pictures of different ethnicities and comparing their proportional face ratio to the divine ratio will help me distinguish a trend in uniqueness from each ethnicity and how well they approximate to the divine ratio. Therefore, I am trying to disprove that not all ethnicities are calculated with phi. My predictions include that each ethnicity will have its own unique ratio. In contrast, each ethnic group might have different characteristics, which might result in different equations.

Methodology

Materials

1) A Computer, which has the Paint program

2) Digital Camera to take pictures

3) A logbook to record all calculations

Procedures

1. Gather multiple pictures of male and females from different ethnicities.

2. Upload pictures into paint.

3. Measure the distance from cheek to cheek ( width)

4. Measure from the top of the head to the bottom of the chin ( height).

5. Put the two measurements in a ratio ( head o chin divided by cheek to cheek) to find the proportions of the face.

6. Find the proportion of the width of the cheek to the width of the mouth.

7. Finally, find the proportion of the width of the mouth.

8. Compare the proportions found on steps five, six, and seven with phi.

9. Compare and contrast between each gender from race to ethnicity and identify whether or not a correlation exists between each ethnicity and how much they deviate from phi.

Results

Conclusion

Appendix A

Caucasian Proportionalities

Appendix B

South Asian Proportionalities

Appendix C

East Asian Proportionalities

Appendix D

African American Proportionalities

Appendix E

Hispanic Proportionalities

Bibliography

A-Stegun, I. ( 2000) . Handbook of Mathematical Functions. New York

Golden Ratio ( n.d.). Retrieved September 7. 2006 from

__http://mathworld.wolfram.com/GoldenRatio.html__

Herz-Fischler, R.( 1998). The Divine Proportion. California

Sydney.(2004). The mathematical formula for the perfect face! Retrieved

September 6, 2006, from __http://www.cojoweb.com/phi/html__

The Human Face.( n.d.). Retrieved September 7, 2006, from

http://www.goldennumber.net

Acknowledgements

I would like to take this time to acknowledge Mrs. Wilson and Mrs. Epperson for all of their support and assistance towards my project. In addition, I would like to thank everyone who volunteered to participate in my experiment; I could not have done it without you, so I appreciate you’re your involvement.