The document discusses how mathematical ratios, specifically the golden ratio, relate to perceptions of beauty. It explains that the human body and faces that are most symmetrical and follow proportions aligned with the golden ratio are deemed more attractive. The golden ratio can be seen in things like the Vitruvian Man illustration and is also present in ratios between different facial features like the eyes, nose, and lips. While no single person perfectly matches all golden ratio proportions, being closer to more of these ratios makes someone's appearance more aligned with traditional standards of beauty.

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 someone’s face and find it beautiful if it
is more proportional!
This idea dates back to the 1490’s, 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: Φ = 1.618 033…(a.k.a phi)
It is an irrational number like pi (𝜋)
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. LET’S TRY SOME
CELEBRITIES!
Guess if the
celebrity is beautiful
or not!!!

15. Joseph Gordon-
Levitt is almost
perfect except for
his eyes. But that’s
okay, I still think
he’s 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
doesn’t know that
Zac Efron is
perfect in every
single way! (Just
not
mathematically…)

19. Looks like
Jennifer
Lawrence isn’t
as perfect as her
acting skillz!

20. Oh, so close
Ms.Ahmad! You
are just a hair
away from being
100% beautiful,
but don’t worry,
you’re perfect in
my eyes!