1. THE MATH BEHIND BEAUTY By: Michelle Berkovich

2. WHAT IS BEAUTY? 3. HOW DOES ONE KNOW WHAT IS PLEASING/BEAUTIFUL? It has to do with math, of course! We are attracted to people who have a symmetrical body. The reason for that is humans are programmed to perceive proportional bodies as more healthy. We are more likely to notice someones face and find it beautiful if it is more proportional! This idea dates back to the 1490s, when Leonardo da Vinci created the Vitruvian Man. 4. THE VITRUVIAN MAN This drawing depicts what the ideal body should look like: eight heads high and symmetrical from foot to naval and naval to head. The ratio (foot to naval):(naval to head) is known as the golden ratio. 5. THE GOLDEN RATIO The golden ratio is based off of the Fibonacci Sequence, where every number in the series is the sum of its previous two numbers. (ex. 1, 1, 2, 3, 5, 8, 13, 21, ...) The ratio of every two neighboring numbers eventually leads to what is known as the golden ration: = 1.618 033(a.k.a phi) It is an irrational number like pi () How to get this ratio 1/1=1 2/1=2 3/2=1.5 5/3=1.666... 8/5=1.6 13/8=1.625 21/13=1.61538... 34/21=1.61905... 55/34=1.61764... 89/55=1.61861.. And so on 6. WHAT DOES THE GOLDEN RATIO HAVE TO DO WITH BEAUTY? The proportions of the length of the nose, the position of the eyes and the length of the chin, all have to equal the golden ration in order to appear beautiful to the human eye. Some of the ratios that determine ones beauty are (top of head to chin):(width of head), (top of head to pupil):(pupil to lip), (nose tip to chin):(lips to chin), (nose tip to chin):(pupil to nose tip), (width of nose):(nose tip to lips), (outside distance between eyes):(hairline to pupil), (length of lips):(width of nose), and many, many more. If the ratios of these features of your face equal the golden ratio, then you are considered beautiful. 7. Architects and artists have been using the golden ratio in their work for years in order to create physically appealing work! Michelangelo's "David statue and the Parthenon in Greece are two examples that use the golden ratio. OOPS 8. GOLDEN RATIO CONTINUED Scientists and mathematicians have created several masks that you can simply place on a picture of yourself in order to determine if you are beautiful. The different ratios are already measured out on these masks in order to equal the golden ratio. 9. ARE YOU BEAUTIFUL? 10. MY FACE a = Top-of-head to chin = 21cm b = Top-of-head to pupil = 10.5 cm c = Pupil to nose tip = 4.5 cm d = Pupil to lip = 8 cm e = Width of nose = 5 cm f = Outside distance between eyes = 11 cm g = Width of head = 13.5 cm h = Hairline to pupil = 6.5 cm i = Nose tip to chin =6 cm j = Lips to chin = 3.5 cm k = Length of lips =2 cm l = Nose tip to lips = 3 cm a/g =1.556 cm b/d = 1.313 cm i/j = 1.714 cm i/c = 1.333 cm e/l =1.667 cm f/h =1.692 cm k/e =0.4 cm 11. AS YOU CAN SEE, I AM NOT AS BEAUTIFUL AS I APPEAR TO BE BECAUSE I ONLY HAD TWO RATIOS THAT ALMOST MATCHED UP WITH THE GOLDEN RATIO. 12. NOW LETS TRY A MASK THAT HAS BEEN PRECISELY MEASURED 13. The mask only slightly matches up with my face: mainly my nose area. Every where else, the mask if off by a little. I tried to manipulate it so it would fit my face, but this was the best it would fit. This goes along with the calculations I made on the previous slide. 14. LETS TRY SOME CELEBRITIES! Guess if the celebrity is beautiful or not!!! 15. Joseph Gordon- Levitt is almost perfect except for his eyes. But thats okay, I still think hes beautiful! 16. Louis Tomlinson of One Direction is the definition of beauty!!! 17. What a surprise?!? Lea Michele is not as perfect as she seems. 18. WOW look at that beauty!!! But who doesnt know that Zac Efron is perfect in every single way! (Just not mathematically) 19. Looks like Jennifer Lawrence isnt as perfect as her acting skillz! 20. Oh, so close Ms.Ahmad! You are just a hair away from being 100% beautiful, but dont worry, youre perfect in my eyes!