Asymmetry:A Hidden Beauty Within Symmetry 1. Introduction 2. The Motif: Types of Symmetries I. Bilateral II. Translational III. Rotational 3. Variation.

Asymmetry:A Hidden Beauty Within Symmetry

1. Introduction2. The Motif: Types of Symmetries

I. BilateralII. TranslationalIII. Rotational

3. Variation on the Theme: Handedness4. Enjoying the Symphony: The Ultimate

Design5. Conclusion

OUTLINEOUTLINE

1.Introduction1.Introduction• Humans: Desire for order and

perfection.

• Symmetry: Implies harmony

• Aristotelian View: “The middle measure” virtue through action.

•The sphere became the symbol for the most perfect geometric shape

2. THE MOTIF2. THE MOTIF•Types of Symmetries:

• Bilateral

• Translational

• Rotational

Symmetry:A Visual Presentation

I. LINE OR BILATERAL SYMMETRY

I. LINE OR BILATERAL SYMMETRY

Line Symmetry• Shape has line symmetry when one half

of it is the mirror image of the other half.

• Symmetry exists all around us and many people see it as being a thing of beauty.

Is a butterfly symmetrical?

At the  beach there are a variety of shells with

line symmetry.

Under the sea there are also many symmetrical objects

such as these crabs

and this starfish.

Animals that have Line Symmetry

Here are a few more great examples of mirror image in the animal kingdom.

Human Symmetry

The 'Proportions of Man' is a famous work of art by Leonardo da Vinci

that shows the symmetry of the human form.

THESE MASKS HAVE SYMMETRY

These masks have a line of symmetry from the forehead to the

chin.  

The human face also has a line of symmetry in the same place.

REFLECTION IN WATER

If an object is reflected in water it

is considered to have line

symmetry along the waterline.

The Taj Mahal

Symmetry exists in architecture all around the world.  The best known example of this is the Taj Mahal.

This photograph shows 2 lines of symmetry. One vertical, the other along

the waterline.

(Notice how the prayer towers, called minarets, are reflected in the water and side to side).

2D Shapes and Symmetry

an equilateral triangle has 3 internal angles and 3 lines of symmetry. 

    a square has 4 internal angles and 4

lines of symmetry.   

  a regular pentagon has 5 internal angles and 5 lines of symmetry.

a regular hexagon has 6 internal angles and 6 lines of symmetry .

    a regular octagon has 8 internal angles and 8 lines of symmetry.

II. TRANSLATIONAL SYMMETRY

II. TRANSLATIONAL SYMMETRY

H

H H

O

Base

PO O

O

O

O CH2

H

H H

O

Base

PO O

O

O

CH2

H

H H

O

Base

PO O

O

O

CH2

H H

HH

H H

{

{

{

DNA MOLECULE

III. ROTATIONAL SYMMETRY

3. HANDEDNESS3. HANDEDNESS

Mirror Images, nonsuperimposable

Mirror Images, nonsuperimposable

• Mirror Images, nonsuperimposable

• Only the helix on the right is DNA

Why Asymmetry?

ObservationsObservations•Why does a mirror reverse only the left and right sides of things, not up and down?

•Why all modern dice are left handed?

•The “monopole problem” of not finding a single north or a single south magnetic charge is still a mystery.

•Nature seems to favor vertical symmetry as seen through the force of gravity operating only straight up and down.

•Interestingly, Western art is dominant with vertical symmetry while Japanese and Chinese art tries to avoid symmetry.

•Most profiles of faces in art face left.

•Most right-handed people prefer to draw left-facing profiles.

•Water flowing in a bath tub at the north pole tend to spiral down the drain in a counterclockwise fashion.

•In the northern half of the globe, cyclones and tornadoes tend to spin counterclockwise.

•Thousands of animals have right - or left-handed helices. Ex.

–the right-handed mollusk shells

–some female birds exhibit only a left ovary

–the halibut is a right-eyed while the flounder is a left-eyed fish

–the analeps (fish) has an asymmetric sex life

•the right lung is larger than the left

•In humans, the left testicle usually hangs lower than the right

•the heart, stomach, and pancreas are shifted more towards the left

•the liver and appendix are on the right

•twists and turns of the intestines are completely asymmetric

•In 1848 Pasteur recognized that organic compounds of living things are asymmetric.

•All amino acids in living tissues have the same left-handed twist

C

COONH3

R

H

•Only the right-handed lactic acid is oxidized to pyruvic acid

CH3

C

COOH

OH

H

•Only the left-handed adrenaline is a cardiac stimulant

H

C

CH2NHCH3

OH

OH

OH

• Left-handed carvone smells like spearmint

• Right-handed carvone smells like caraway

CH3

O

CCH3

CH2

CH3

O

C

CH2

CH3

Pasteur Wrote:• “Life ,as manifested to us, is a

function of the asymmetry of the universe and of the consequences of this fact....I can even imagine that all living species are primordially, in their structure, in their external forms, functions of cosmic asymmetry.”

•Pasteur believed that some sort of basic asymmetry in the earth’s environment was responsible for the left-right bias of organic compounds.

•He was fascinated by the sharp conflict between the symmetry of nonlife and the asymmetry of life.

•He believed that if he could only discover how nature introduced this asymmetry into organic compounds, he would be close to the secret of life itself.

Here are possible explanations:Here are possible explanations:

• Life began in one hemisphere, where the Coriolis forces may have provided the required twist. Had life started in the other hemisphere, the amino acids would now be right-handed instead of left.

•Elliptically polarized light may have combined with the earth’s magnetic field to supply the twist

• Russian scientist V. Vernadski suggested in 1931:

–That the moon was separated from earth causing a left-handed twist to organic molecules

• Physicist Joseph Rush in his book The Dawn of Life suggested (Signet,1962):

–That perhaps self-replicating molecules of both handedness evolved in the primordial soup. A mutation of one left-handed molecule gave it the ability to cause the twist

So What?So What?

•Three Assertions

• That Patterns of symmetry are not fundamental laws of nature

•That Patterns of symmetry are only a manifestation of

a philosophical and mathematical attitude cultivated by the ancient Greeks and the far easterners.

•That Nature, apparently, is completely ambidextrous

Beauty and the Beast

Thank you

Professor

Salim M. Diab

University of St. Francis

815-740-3855

[email protected]