TOK Looking Glass Presentation Mathematics and Beauty - made by Professor Daniel Cohen-Or at Tel Aviv University.

- altering the proportions of pre-existing features

- aesthetic quality of facial features can be quantified using mathematics.

Professor Daniel Cohen-Or says:

“I don't claim to know much about beauty. For us, every picture in this research project is just a collection of numbers." The Beauty Machine Links to Images used: http://library.thinkquest.org/trio/TTQ05063/monalisa.gif

http://www.aftau.org/site/News2?page=NewsArticle&id=7899

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

http://www.seven-pride.com/uploads/editor/News_Images/sculptures/9_venus_de_milo.jpg Ivy He, Lucy Li, Claire Ping, Sakshi Singh, Amanda Tam How does mathematical patterns and formulas reflect human behaviour? CENTRAL

KNOWLEDGE

ISSUE Does mathematical explanation enhance or hinder our understanding of the

natural world? First Discussion Question Does logical thinking in mathematics and mathematical theories help us to have a more enhanced perception of the natural world? Different aspects of the natural world can be considered, such as culture and human behavior. Pros:

enhance our understanding of the natural world

Ex. Statistics can be applied to psychology studies.

summarize certain things, create applicable patterns, and make connections

Ex. Real life situation related to beauty: the Golden Ratio (found in human facial structure); dance of bees.

Con:

hinders our understanding of the natural world.

Theoretical: many mathematical explanations are not applicable in the real world

Lacks emotional responses

Create categories, divisions, disregarding that in nature, everything is related to each other.

Lead to false implications sometimes. And the Fibonacci Sequence The Golden Ratio 1 : 0.61803... 1 : 1.61803... = BEAUTY and/or Is mathematics existent in nature

or a human creation? Second Discussion Question Math exists in nature:

Shapes & patterns in nature

Math also exists in the form of the Golden Ratio, as we have just explained, and the Fibonacci Sequence.

Applied math --> science (chemistry, biology, and physics).

Math is a human creation:

Number symbols

The entire math system is based on axioms.

Expression of certain patterns

Ex. Our Real-life situation: Beauty

It describes what occurs in nature. Does mathematics explain nature and reality

better than other subject areas,

specifically the arts? Third Discussion Question Mathematics:

Depict nature in a systematic way:

Labeling and categorizing things in nature

Better depict nature --> produces a rather objective and unbiased reflection of reality

Lack emotions/Subjective

Art:

The artist’s perception of reality

Emotions and objectivity --> Emotions enhance understanding

Ex. Literature: emotional response to author's emphasis of a theme

Mathematicians argue that mathematics is an art. This is indeed true as both mathematics, especially pure math, and the arts attempt to make sense of nature through an abstract way or by producing an abstract reflection of what the mathematician or artist perceive of the world. Does mathematics change with changes in human behaviours? How do they affect each other? Fourth Discussion Question Some (even all?) mathematical concepts stay constant because human nature does

For example: most attractive women --> waist-to-hip ratio of approximately 0.7 (waist being 70% in size of the hips)

Examples: Jessica Alba, Marilyn Monroe and even Michelangelo’s Venus de Milo

This mathematical concept has stayed constant along with human behaviour, unchanged in its preference of beauty. When is mathematical patterns and formulas not applicable in the real world? What can it not explain? Fifth Discussion Question Applied mathematics is applicable in the real world

However, pure mathematics is also applicable in the real world --> attempts to explain patterns seen in nature.

Ex. Geometry

Mathematics cannot explain abstract concepts such as imagination

math is based on logical thinking

Imagination follows no specific patterns and is not rational like mathematics.

Math also can not give us emotional knowledge

Ex. Crime and Punishment Mathematical Formulas:

enhance our understanding of the natural world.

are human creations, but nonetheless attempt to explain the world.

Mathematicians strive to discover patterns

are sometimes not applicable to the real world (emotion, imagination)

Mathematics

exists in nature

affects human behavior and human behavior affects human behaviour

remains unchanged as human behaviour remains constant

changes over time (axioms) THANK YOU

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# TOK Presentation - Mathematics

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