The Golden Ratio

By Akshat Rajan

What is Golden Ratio?

• The golden ratio is an irrational number. If a person tries to write it, they will never stop and never be the same again and again, but it will start this way- 1.6180339887...(approximately) An important thing about this number is that a person can subtract 1 from it or divide 1 by it. Either way, he will find the same number. Math is related to everything. In this presentation you will learn how its related to beauty. You can call somebody beautiful using math too. The golden ratio is 1:1.6.

MY FACEBridge Width=15mm Eye Width=14 mmBridge/Eye Ratio=15:14Mouth Width=18mmTeeth Width=16mmMouth/Teeth Ratio=9:8The 2 ratios are not same but

are a bit close.

Comparing Faces (9 classmates)Name: Bridge

Width (mm)Eye Width (mm)

Bridge/Eye Ratio

Mouth Width(mm)

Teeth Width(mm)

M/TRatio

Aditya 0.3 0.3 0.3:0.3 0.9 0.5 0.9:0.5

Arnav 35 30 7:8 75 60 5:4

Akshat 30 36 5:6 40 25 8:5

Jahnavi 35 25 7:5 60 50 6:5

KaevaanAkash 40 40 1:1 70 45 14:9

Ratisha 42 37 42:37 79 49 79:49

Nishna 60 40 3:2 90 60 3:2

Siddhant 35 35 1:1 75 60 5:4

Class Mates

• Total B/E Ratio=66:60• Average=11:30 • Total M/T Ratio=120:78• Average=20:13 • These ratios were mostly different but a

few were similar.They were little different. The average is 20:13. In one, Nishna’s its exact the others are similar but not all.

Adult Face My MomBridge Width=15mm Eye Width=14 mmBridge/EyeRatio=15:14Mouth Width=18mmTeeth Width=16mmMouth/TeethRatio=9:8

3 celebrities

Name: Bridge Eye B/E Ratio

Mouth Teeth M/T Ratio

Diana Argon

30 50 3:5 80 60 8:6

Deepika Pudokone

22 20 11:10 32 20 16:13

Bipasha Basu

70 80 7:8 12 10 6:5

• The result is not that different.• My moms and the actresses aren't far

apart! So maybe because my mom is beautiful.

In Nature

• Ancient Greek- Partheron

• IN THIS STAMP, This stamp is proportional! It is exactly made according to the golden ratio!

• This is the sunflower which is in the golden ratio! When it’s a simple fraction The pattern of seeds are spirals.

Many Paintings too!

Her face is exactly the golden rectangle!! the ratio of the width of her forehead compared to the length from the top of her head to her chin.

So math is even used while making a painting! (Interdisciplinary)

The human body!!

• We have 2 eyes 2 pairs of limbs, a nose etc. All these parts can also be divided up in terms of the golden ratio! So imagine the amount of things with math behind it. This power point simply proves the math is everywhere, even when we don’t want to be there, its THERE!!

• Places like the Pyramid of Giza, the UN building in New York! Are also in golden ratio!

Every 10 floors are in the golden ratio!

Math even comes in Architecture!

Reflection• I think this investigation was very essential it

actually showed us how math is ‘the’ most important subject in our lives. Even if we hate it, its there and if we don’t learn now we will never! So I think this investigation was beyond ratio and proportion as it explained the importance and significance of math and all the different parts of it like ratio! I did not have any difficulties in this but was a bit confused. This is related to our AOI Human Ingenuity as golden ratio is created by us!

Bibliography

• http://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html

• http://science.howstuffworks.com/evolution/fibonacci-nature1.htm

• http://library.thinkquest.org/trio/TTQ05063/phibeauty3.htm

• http://library.thinkquest.org/trio/TTQ05063/phibeauty4.htm